Chapter 1: Q. 26 (page 29)

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.
$(x + 2) (x - 3) = {(x - 3)}^{2}$

Short Answer

Expert verified

The required solution is $x = 3$ and the graph of the solution is given below:

Step by step solution

Step 1. Given information.

We have:

$(x + 2) (x - 3) = {(x - 3)}^{2}$

Step 2. Solve the equation algebraically.

The solution of the equation is $(x + 2) (x - 3) = {(x - 3)}^{2}$ .

Expand:

$x^{2} - x - 6 = x^{2} - 6 x + 9$

Add $6$ to both sides:

$x^{2} - x - 6 + 6 = x^{2} - 6 x + 9 + 6 x^{2} - x = x^{2} - 6 x + 15$

Subtract $x^{2} - 6 x$ from both sides:

$x^{2} - x - (x^{2} - 6 x) = x^{2} - 6 x + 15 - (x^{2} - 6 x) 5 x = 15 \frac{5 x}{5} = \frac{15}{5} x = 3$

Step 3. Verify the solution using a graphing utility.

The solution of the equation is $x = 3 .$

Draw the graph of the equation $(x + 2) (x - 3) = {(x - 3)}^{2}$ using the graphing utility:

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In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.
$(x + 2) (x - 3) = {(x - 3)}^{2}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the equation algebraically.

Step 3. Verify the solution using a graphing utility.

One App. One Place for Learning.

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In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.x+2x-3=x-32

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the equation algebraically.

Step 3. Verify the solution using a graphing utility.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Decision Maths

Mechanics Maths

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.
$(x + 2) (x - 3) = {(x - 3)}^{2}$