Chapter 9, Problem 22MCQ

To determine

To solve the given equation by factoring.

Answer to Problem 22MCQ

The value of x is -7 .

Explanation of Solution

Given information :

The equation provided is $x^2+14x+49=0$ .

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 :

  $x^2+14x+49=0$

Given equation.

  $=>x^2+7x+7x+49=0$

Breaking the middle term.

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

Arranging the common factors.

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

The two factors of the function.

  $=>{\left(x+7\right)}^2=0$

Now, the root is:

  $x+7=0$

Using zero-product property.

  $x=-7$

This is the value of x . Since both the factors are same, there is only one value of the equation.