Impact Mathematics Algebra and More

McGraw Hill

Chapter 7

Solving Quadratic Equations - all with Video Answers

Educators

Section 1

Solving by Backtracking

Problem 1

Consider the equation $-\sqrt{2 x-1}=-7$
a. Draw a flowchart for the equation.
b. Solve the equation by backtracking.

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 2

Solve each equation.
$$
\sqrt{3 x+1}=4
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 3

Solve each equation.
$$
\frac{2}{3 p-1}=5
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 4

Solve each equation.
$$
\sqrt{a}=1.5
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 5

Solve each equation.
$$
\sqrt{2-q}=2.5
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 6

Solve each equation.
$$
5 \sqrt{\frac{z}{5}-1}=4
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 7

Solve each equation.
$$
\frac{9}{4-7 d}=18
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 8

Solve each equation.
$$
2(x-4)^{2}+5=7
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 9

Solve each equation.
$$
b^{2}-5=44
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 10

Solve each equation.
$$
c^{2}-20=44
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 11

Solve each equation.
$$
(L-2)^{2}-5=44
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 12

Solve each equation.
$$
(q-2)^{2}+8=44
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 13

Solve each equation.
$$
y^{3}=27
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 14

Solve each equation.
$$
3(2 w-3)^{2}-5=70
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 15

Solve each equation.
$$
(2 t-3)^{2}-20=44
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 16

$$
y^{3}=-27
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 17

Solve each equation.
$$
(x+2)^{3}=64
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 18

A man controlling a robot with a camera eye has just sent it into a burning house to retrieve a safe full of money. He has given it this set of commands:
Forward 20 feet.
Right turn.
Forward 15 feet.
Left turn.
Forward 30 feet.
Right turn.
Forward 25 feet.
Pick up safe.

Jacob Shpiece

Numerade Educator

Problem 19

Mary Ann used her calculator to find $\sqrt{2},$ wrote down the result, and then cleared the calculator. She then used her calculator to square the number she had written down, and got $1.99998 .$ Mary Ann concluded that squaring doesn't exactly undo taking the square root. Do you agree with her? What would you tell her?

M S

Numerade Educator

Problem 20

Many equations cannot be solved directly by backtracking. Some have the variable stated more than once; others involve variable as exponents. Here are some equations that can't be solved directly by backtracking.
$$
\begin{array}{c}{f^{2}=f+1} & {x=\sqrt{x}+1 \quad k^{2}+k=0} \\ {1.1^{B}=2} & {\frac{1}{x}=x^{2}+2}\end{array}
$$
For each equation below, write yes if it can be solved directly by backtracking and $n o$ if it cannot.
$$
\begin{array}{ll}{\text { a. } 5=\sqrt{x-11}} & {\text { b. } 4^{d}=9} \\ {\text { c. } 3 g^{2}=5} & {\text { d. } \sqrt{x+1}=x-4}\end{array}
$$

Melissa Lupinacci

Melissa Lupinacci

Numerade Educator

Problem 21

Use backtracking to solve the equations in Parts a and b.
a. $(3 x+4)^{2}=25$
b. $(3 x+4)^{2}=0$
c. How many solutions did you find for each equation? Can you explain the difference?

Shaza Hammoud

Numerade Educator

Problem 22

Use backtracking to solve the equations in Parts a and b.
a. $(\sqrt{x})^{2}=5$
b. $\sqrt{x^{2}}=5$
c. How many solutions did you find for each equation? Can you explain the difference?

Arielle Vanarsdall

Arielle Vanarsdall

Numerade Educator

Problem 23

Expand each expression.
$$
3(3 a-7)
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 24

Expand each expression.
$$
-2 b(8 b-0.5)
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 25

Expand each expression.
$$
9 c(-8+7 c)
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 26

Expand each expression.
$$
(d+3)(d+6)
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 27

Expand each expression.
$$
(2 e-4)(e-6)
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 28

Expand each expression.
$$
(3 f+10)(9 f-1)
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 29

Expand each expression.
$$
(g+7)^{2}
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 30

Expand each expression.
$$
(3 h-1)^{2}
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 31

Expand each expression.
$$
(2 j+2)^{3}
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 32

Expand each expression.
$$
(3 k-2 m)^{2}
$$

Sriram Soundarrajan

Sriram Soundarrajan

Numerade Educator

Problem 33

Find the area of each rectangle.

Katie Hassett

Numerade Educator

Problem 34

Find the area of each rectangle.

Katie Hassett

Numerade Educator

Problem 35

Life Science The table lists the approximate amount of dry plant material that each type of habitat produces in 1 year.
$$
\begin{array}{ll}{} & {\text { Plant Material (grams) }} \\ {\text { Habitat }} & {\text { Produced per Square Meter }} \\ {\text { Coral reef }} & {2,500} \\ {\text { Tropical rainforest }} & {2,200} \\ {\text { Temperate rainforest }} & {1,250} \\ {\text { Savannah }} & {900} \\ {\text { Open sea }} & {125} \\ {\text { Semidesert }} & {90}\end{array}
$$
a. One gram is equivalent to 0.035 ounce, and 1 meter is equivalent to 1.09361 yards. Determine how many ounces of plant material per square yard the typical coral reef produces in 1 year. Show
how you found your answer.
b. Write two different statements comparing the amount of plant material produced in a tropical rain forest to that produced in a temperate rain forest.
c. The Baltic Sea covers approximately $422,000$ square kilometers. Approximately how many kilograms of plant material are produced in the Baltic Sea in a year? Show how you found your answer.

Rikhil Makwana

Numerade Educator