Chapter 9.5, Problem 19PPS

To determine

Find the solution.

Answer to Problem 19PPS

$x=-8$ or $x=2$

Explanation of Solution

Given Information: $x^2+6x-16=0$

Formula Used: $a^2+2ab+b^2={(a+b)}^2$ and $a^2-b^2=(a+b)(a-b)$

Calculation:

  $x^2+6x-16=0$

Now, adding & subtracting the square of half the coefficient of x.

  $x^2+6x-16+{\left(\frac{6}{2}\right)}^2-{\left(\frac{6}{2}\right)}^2=0$

Now use formula, $a^2+2ab+b^2={(a+b)}^2$

  ${\left(x+3\right)}^2-16-3^2=0$

So,

  ${\left(x+3\right)}^2-16-9=0$

So,

  ${\left(x+3\right)}^2-25=0$

Now, square root of 25 is 5

  ${\left(x+3\right)}^2-{\left(5\right)}^2=0$

Now use formula, $a^2-b^2=(a+b)(a-b)$

  $\left(x+3+5\right)\left(x+3-5\right)=0$

Now,

  $\left(x+8\right)\left(x-2\right)=0$

Hence,

$x=-8$ or $x=2$