Chapter 9, Problem 37SGR

To determine

To solve the given equation by factoring.

Answer to Problem 37SGR

The value of x is -7 and 1 .

Explanation of Solution

Given information :

The equation provided is $x^2+6x+9=16$ . This can be written as $x^2+6x-7=0$ , by subtracting 16 from both sides.

Formula used :

The given equation can be solved by factoring. To do so, break up the midpoint to arrive at two factors. Then use the zero-product property to equate each factor in order to get the roots.

Calculation :

  $x^2+6x-7=0$

Equation to be solved.

  $=>x^2+7x-x-7=0$

Breaking the middle term that when multiplied, provides that values of $a{x}^2\times c$ .

  $=>x\left(x+7\right)-1\left(x+7\right)=0$

Arranging the common factors.

  $=>\left(x-1\right)\left(x+7\right)=0$

The two factors of the function.

Now, the first root is:

  $x-1=0$

Using zero-product property.

  $x=1$

The second root is:

  $x+7=0$

Using zero-product property.

  $x=-7$

Thus, the values of x are -7 and 1 .

To check the solutions, put them in the given equation and verify that left-hand and right-hand sides are equal.

For $x=1$

  ${\left(1\right)}^2+6\left(1\right)-7=0$

Putting the value in the equation.

  $=>1+6-7=0$

Simplifying the expression.

  $=>7-7=0$

Hence this result is a success.

Now, for $x=-7$

  ${\left(-7\right)}^2+6\left(-7\right)-7=0$

Putting the value in the equation.

  $=>49-42-7=0$

Simplifying the expression.

  $=>49-49=0$

Hence this result is a success.