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Q. 25

Expert-verifiedFound in: Page 29

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

$\left(x+7\right)\left(x-1\right)={\left(x+1\right)}^{2}$

The required solution is $x=2$ and the graph of the solution is given below:

We have:

$\left(x+7\right)\left(x-1\right)={\left(x+1\right)}^{2}$

The equation is $\left(x+7\right)\left(x-1\right)={\left(x+1\right)}^{2}.$

Expand:

${x}^{2}+6x-7={x}^{2}+2x+1$

Add $7$ to both sides:

${x}^{2}+6x-7+7={x}^{2}+2x+1+7\phantom{\rule{0ex}{0ex}}{x}^{2}+6x={x}^{2}+2x+8$

Subtract ${x}^{2}+2x$ to both sides:

${x}^{2}+6x-\left({x}^{2}+2x\right)={x}^{2}+2x+8-\left({x}^{2}+2x\right)\phantom{\rule{0ex}{0ex}}4x=8\phantom{\rule{0ex}{0ex}}\frac{4x}{4}=\frac{8}{4}\phantom{\rule{0ex}{0ex}}x=2$

The solution of the equation is $x=2.$

Draw the graph of the equation $\left(x+7\right)\left(x-1\right)={\left(x+1\right)}^{2}$ using the graphing utility:

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