Chapter 9.5, Problem 21PPS

To determine

Find the solution.

Answer to Problem 21PPS

  $x=-1$ or $x=9$

Explanation of Solution

Given Information: $x^2-8x-1=8$

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

Calculation:

  $x^2-8x-1=8$

So, simplify

  $x^2-8x-1-8=0$

Now,

  $x^2-8x-9=0$

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

  $x^2-8x-9+{\left(\frac{8}{2}\right)}^2-{\left(\frac{8}{2}\right)}^2=0$

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

  ${\left(x-4\right)}^2-9-4^2=0$

So,

  ${\left(x-4\right)}^2-9-16=0$

So,

  ${\left(x-4\right)}^2-25=0$

Now, square root of 25 is $5$

  ${\left(x-4\right)}^2-{\left(5\right)}^2=0$

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

  $\left(x-4+5\right)\left(x-4-5\right)=0$

Now,

  $\left(x+1\right)\left(x-9\right)=0$

Hence,

  $x=-1$ or $x=9$