Chapter 9.5, Problem 6CYU

To determine

Find the solution.

Answer to Problem 6CYU

  $x=1.4$ or $x=6.6$

Explanation of Solution

Given Information: $x^2-8x=-9$

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

Calculation:

  $x^2-8x=-9$

So,

  $x^2-8x+9=0$

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,

  ${\left(x-4\right)}^2-7=0$

Now, square root of 7 is $\sqrt{7}$

  ${\left(x-4\right)}^2-{\left(\sqrt{7}\right)}^2=0$

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

  $\left(x-4+\sqrt{7}\right)\left(x-4-\sqrt{7}\right)=0$

So,

  $x=4-\sqrt{7}$ or $x=4+\sqrt{7}$

Hence,

  $x=1.35$ or $x=6.64$

Nearest tenth = $x=1.4$ or $x=6.6$