Chapter 9.5, Problem 20PPS

To determine

Find the solution.

Answer to Problem 20PPS

  $x=-2.9$ or $x=4.9$

Explanation of Solution

Given Information: $x^2-2x-14=0$

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

Calculation:

  $x^2-2x-14=0$

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

  $x^2-2x-14+{\left(\frac{2}{2}\right)}^2-{\left(\frac{2}{2}\right)}^2=0$

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

  ${\left(x-1\right)}^2-14-1^2=0$

So,

  ${\left(x-1\right)}^2-14-1=0$

So,

  ${\left(x-1\right)}^2-15=0$

Now, square root of 15 is $\sqrt{15}$

  ${\left(x-1\right)}^2-{\left(\sqrt{15}\right)}^2=0$

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

  $\left(x-1+\sqrt{15}\right)\left(x-1-\sqrt{15}\right)=0$

Now,

  $\left(x+2.87\right)\left(x-4.87\right)=0$

Hence,

  $x=-2.87$ or $x=4.87$

Nearest Tenth $x=-2.9$ or $x=4.9$