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Section 1

Solving Quadratic Equations by the Square Root Property

Which of the following are quadratic equations?A. $x+2 y=0$B. $x^{2}-8 x+16=0$C. $2 t^{2}-5 t=3$D. $x^{3}+x^{2}+4=0$

Which quadratic equation identified in Exercise 1 is in standard form?

A student incorrectly solved the equation $x^{2}-x-2=5$ as follows.WHAT WENT WRONG?$\begin{aligned} x^{2}-x-2 &=5 \\(x-2)(x+1) &=5 \\ x-2=5 & \text { or } x+1=5 \\ x=7 & \text { or } \quad x=4 \end{aligned}$ Factor.Zero-factor propertySolve each equation.

A student was asked to solve the quadratic equation $x^{2}=16$ and did not get full credit for the solution set $\{4\} .$ WHAT WENT WRONG?

Solve each equation by the zero-factor property. See Example 1 .$$x^{2}-x-56=0$$

Solve each equation by the zero-factor property. See Example 1 .$$x^{2}-2 x-99=0$$

Solve each equation by the zero-factor property. See Example 1 .$$x^{2}=121$$

Solve each equation by the zero-factor property. See Example 1 .$$x^{2}=144$$

Solve each equation by the zero-factor property. See Example 1 .$$3 x^{2}-13 x=30$$

Solve each equation by the zero-factor property. See Example 1 .$$5 x^{2}-14 x=3$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$x^{2}=81$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$z^{2}=169$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$x^{2}=14$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$m^{2}=22$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$t^{2}=48$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$x^{2}=54$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$x^{2}=\frac{25}{4}$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$m^{2}=\frac{36}{121}$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$x^{2}=2.25$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$w^{2}=56.25$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$r^{2}-3=0$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$x^{2}-13=0$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$x^{2}-20=0$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$p^{2}-50=0$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$7 x^{2}=4$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$3 p^{2}=10$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$3 n^{2}-72=0$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$5 z^{2}-200=0$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$5 x^{2}+4=8$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$4 p^{2}-3=7$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$2 t^{2}+7=61$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$3 x^{2}+8=80$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$-8 x^{2}=-64$$

Solve each equation by using the square root property. Simplify all radicals. See Example 2.$$-12 x^{2}=-144$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(x-3)^{2}=25$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(x-7)^{2}=16$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(x-4)^{2}=3$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(x+3)^{2}=11$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(x-8)^{2}=27$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(p-5)^{2}=40$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(3 x+2)^{2}=49$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(5 t+3)^{2}=36$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(4 x-3)^{2}=9$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(7 z-5)^{2}=25$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(3 x-1)^{2}=7$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(2 x-5)^{2}=10$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(3 k+1)^{2}=18$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(5 z+6)^{2}=75$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(5-2 x)^{2}=30$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(3-2 x)^{2}=70$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$\left(\frac{1}{2} x+5\right)^{2}=12$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$\left(\frac{1}{3} m+4\right)^{2}=27$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(4 x-1)^{2}-48=0$$

Solve each equation by using the square root property. Simplify all radicals. See Examples 4 and 5.$$(2 x-5)^{2}-180=0$$

Use a calculator with a square root key to solve each equation. Round your answers to the nearest hundredth.$$(k+2.14)^{2}=5.46$$

Use a calculator with a square root key to solve each equation. Round your answers to the nearest hundredth.$$(r-3.91)^{2}=9.28$$

Use a calculator with a square root key to solve each equation. Round your answers to the nearest hundredth.$$(2.11 p+3.42)^{2}=9.58$$

Use a calculator with a square root key to solve each equation. Round your answers to the nearest hundredth.$$(1.71 m-6.20)^{2}=5.41$$

Find the non real complex solutions of each equation. See Example 6$$x^{2}=-12$$

Find the non real complex solutions of each equation. See Example 6$$x^{2}=-18$$

Find the non real complex solutions of each equation. See Example 6$$(r-5)^{2}=-4$$

Find the non real complex solutions of each equation. See Example 6$$(t+6)^{2}=-9$$

Find the non real complex solutions of each equation. See Example 6$$(6 x-1)^{2}=-8$$

Find the non real complex solutions of each equation. See Example 6$$(4 m-7)^{2}=-27$$

Round answers to the nearest tenth. See Example 3.The sculpture of American presidents at Mount Rushmore National Memorial is $500 \mathrm{ft}$ above the valley floor. How long would it take a rock dropped from the top of the sculpture to fall to the ground?

Round answers to the nearest tenth. See Example 3.The Gateway Arch in St. Louis, Missouri, is 630 ft tall. How long would it take an object dropped from the top of the arch to fall to the ground?

Solve each problem. See Example 3.The area $\mathscr{A}$ of a circle with radius $r$ is given by the formula$$\mathscr{A}=\pi r^{2}$$If a circle has area $81 \pi$ in. $.$, what is its radius?(FIGURE CANT COPY)

Solve each problem. See Example 3.The surface area $S$ of a sphere with radius $r$ is given by the formula$$S=4 \pi r^{2}$$If a sphere has surface area $36 \pi \mathrm{ft}^{2}$, what is its radius?(FIGURE CANT COPY)

The amount $A$ that $P$ dollars invested at an annual rate of interest $r$ will grow to in 2 yr is$$A=P(1+r)^{2}$$At what interest rate will $\$ 100$ grow to $\$ 104.04$ in 2 yr?

The amount $A$ that $P$ dollars invested at an annual rate of interest $r$ will grow to in 2 yr is$$A=P(1+r)^{2}$$At what interest rate will $\$ 500$ grow to $\$ 530.45$ in 2 yr?

Simplify all radicals, and combine like terms. Express fractions in lowest terms. See Sections $10.3-10.5$$$\frac{4}{5}+\sqrt{\frac{48}{25}}$$

Simplify all radicals, and combine like terms. Express fractions in lowest terms. See Sections $10.3-10.5$$$\frac{12-\sqrt{27}}{9}$$

Simplify all radicals, and combine like terms. Express fractions in lowest terms. See Sections $10.3-10.5$$$\frac{6+\sqrt{24}}{8}$$

Factor each perfect square trinomial. See Section $5.4 .$$$z^{2}+4 z+4$$

Factor each perfect square trinomial. See Section $5.4 .$$$x^{2}-10 x+25$$

Factor each perfect square trinomial. See Section $5.4 .$$$z^{2}+z+\frac{1}{4}$$