Section 1
Solving Quadratic Equations by Completing the Square
Solve each equation or inequality.$\frac{t+9}{2}+\frac{t+2}{5}=\frac{8}{5}+4 t$
Solve each equation or inequality.$\frac{1-5 x}{2 x}+4=\frac{x+3}{x}$
Solve each equation or inequality.$3(t-3)+3 t \leq 2(t+1)+t+1$
Solve each equation or inequality.$-2(y+4)-3 y+8 \geq 3(2 y-3)-y$
Fill in the blanks.If $c>0$, the solutions of $x^2=c$ are ________ and ________
Fill in the blanks.To complete the square on $x$ in $x^2+6 x$, find one-half of ___ , square it to get ___ , and add ____ to get ________ .
Fill in the blanks.The symbol $\pm$ is read as ________ .
Fill in the blanks.The formula for compound interest is ________ .
Use factoring to solve each equation.$6 x^2+12 x=0$
Use factoring to solve each equation.$5 x^2+11 x=0$
Use factoring to solve each equation.$2 y^2-50=0$
Use factoring to solve each equation.$4 y^2-64=0$
Use factoring to solve each equation.$r^2+6 r+8=0$
Use factoring to solve each equation.$x^2+9 x+20=0$
Use factoring to solve each equation.$7 x-6=x^2$
Use factoring to solve each equation.$5 t-6=t^2$
Use factoring to solve each equation.$2 z^2-5 z+2=0$
Use factoring to solve each equation.$2 x^2-x-1=0$
Use factoring to solve each equation.$6 s^2+11 s-10=0$
Use factoring to solve each equation.$3 x^2+10 x-8=0$
Use the square root property to solve each equation.$x^2=36$
Use the square root property to solve each equation.$x^2=144$
Use the square root property to solve each equation.$z^2=5$
Use the square root property to solve each equation.$u^2=24$
Use the square root property to solve each equation.$3 x^2-16=0$
Use the square root property to solve each equation.$5 x^2-49=0$
Use the square root property to solve each equation.$(y+1)^2=1$
Use the square root property to solve each equation.$(y-1)^2=4$
Use the square root property to solve each equation.$(s-7)^2-9=0$
Use the square root property to solve each equation.$(t+4)^2=16$
Use the square root property to solve each equation.$(x+5)^2-3=0$
Use the square root property to solve each equation.$(x+3)^2-7=0$
Use the square root property to solve each equation.$(x-2)^2-5=0$
Use the square root property to solve each equation.$(x-5)^2-11=0$
Use the square root property to solve each equation.$p^2+16=0$
Use the square root property to solve each equation.$q^2+25=0$
Use the square root property to solve each equation.$4 m^2+81=0$
Use the square root property to solve each equation.$9 n^2+121=0$
Use completing the square to solve each equation.$x^2+2 x-8=0$
Use completing the square to solve each equation.$x^2+6 x+5=0$
Use completing the square to solve each equation.$x^2-6 x+8=0$
Use completing the square to solve each equation.$x^2+8 x+15=0$
Use completing the square to solve each equation.$x^2+5 x+4=0$
Use completing the square to solve each equation.$x^2-11 x+30=0$
Use completing the square to solve each equation.$x+1=2 x^2$
Use completing the square to solve each equation.$-2=2 x^2-5 x$
Use completing the square to solve each equation.$6 x^2+11 x+3=0$
Use completing the square to solve each equation.$6 x^2+x-2=0$
Use completing the square to solve each equation.$9-6 r=8 r^2$
Use completing the square to solve each equation.$11 m-10=3 m^2$
Use completing the square to solve each equation.$\frac{7 x+1}{5}=-x^2$
Use completing the square to solve each equation.$\frac{3 x^2}{8}=\frac{1}{8}-x$
Use completing the square to solve each equation.$p^2+2 p+2=0$
Use completing the square to solve each equation.$x^2-6 x+10=0$
Use completing the square to solve each equation.$y^2+8 y+18=0$
Use completing the square to solve each equation.$t^2+t+3=0$
Use completing the square to solve each equation.$3 m^2-2 m+3=0$
Use completing the square to solve each equation.$4 p^2+2 p+3=0$
Find all $x$ that will make $f(x)=0$.$f(x)=2 x^2+x-5$
Find all $x$ that will make $f(x)=0$.$f(x)=3 x^2-2 x-4$
Find all $x$ that will make $f(x)=0$.$f(x)=x^2+x-3$
Find all $x$ that will make $f(x)=0$.$f(x)=x^2+2 x-4$
The distance $s$ (in feet) that an object will fall in $t$ seconds is given by the formula $s=16 t^2$. How long will it take an object to fall 256 feet?
The time (in seconds) it takes a pendulum to swing back and forth to complete one cycle is related to its length $l$ (in feet) by the formula:
$$l=\frac{32 t^2}{4 \pi^2}$$
How long will it take a 5 -foot pendulum to swing through one cycle? Give the result to the nearest hundredth.
To estimate the speed $s$ (in mph) of a car involved in an accident, police often use the formula $s^2=10.5 l$, where $l$ is the length of any skid mark. How fast was a car going that was involved in an accident and left skid marks of 500 feet? Give the result to the nearest tenth.
The approximate pulse rate (in beats per minute) of an adult who is $t$ inches tall is given by the formula
$$p^2=\frac{348,100}{t}$$
Find the pulse rate of an adult who is 64 inches tall.
A student invests $$\$ 8,500$$ in a savings account drawing interest that is compounded annually. Find the annual rate if the money grows to $$\$ 9,193.60$$ in 2 years.
A woman invests $$\$ 12,500$$ in a savings account drawing interest that is compounded annually. Find the annual rate if the money grows to $$\$ 14,045$$ in 2 years.
Explain how to complete the square.
Tell why $a$ cannot be 0 in the quadratic equation $a x^2+b x+c=0$.
What number must be added to $x^2+\sqrt{3} x$ to make it a perfect-square trinomial?
Solve $x^2+\sqrt{3} x-\frac{1}{4}=0$ by completing the square.