Chapter 9.5, Problem 44E

To determine

To solve the Quadratic equation.

Answer to Problem 44E

  $x=1$ or $x=-7$

Explanation of Solution

Given:

Equation:

  $x^2+6x+9=16$

Formula used:

Factoring method.

Calculation:

Converting the given equation in standard form i.e. $a{x}^2+bx+c=0$

  $x^2+6x+9-16=0$

So,

  $x^2+6x-7=0$

Solving equation using factoring method.

  $x^2+6x-7=0$

Split the middle term in such a way that the product comes -7 and sum comes 6

  $x^2-1x+7x-7=0$

Taking common,

  $x(x-1)+7(x-1)=0$

So,

  $(x-1)(x+7)=0$

Therefore,

  $(x-1)=0$ or $(x+7)=0$

so,

  $x=1$ or $x=-7$

Factoring method is easy and less time consuming.