Chapter 9, Problem 35SGR

To determine

To solve the given equation by factoring.

Answer to Problem 35SGR

The value of n is -4 and 2 .

Explanation of Solution

Given information :

The equation provided is $2n^2+4n=16$ . This can be written as $2n^2+4n-16=0$ .

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 :

  $2n^2+4n-16=0$

Given equation.

  $=>\frac{2n^2+4n-16}{2}=\frac{0}{2}$

Dividing both sides by 2.

  $=>n^2+2n-8=0$

Equation to be solved.

  $=>n^2+4n-2n-8=0$

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

  $=>n\left(n+4\right)-2\left(n+4\right)=0$

Arranging the common factors.

  $=>\left(n-2\right)\left(n+4\right)=0$

The two factors of the function.

Now, the first root is:

  $n-2=0$

Using zero-product property.

  $n=2$

The second root is:

  $n+4=0$

Using zero-product property.

  $n=-4$

Thus, the values of n are -4 and 2 .

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

For $n=2$

  ${\left(2\right)}^2+2\left(2\right)-8=0$

Putting the value in the equation.

  $=>4+4-8=0$

Simplifying the expression.

  $=>8-8=0$

Hence this result is a success.

Now, for $n=-4$

  ${\left(-4\right)}^2+2\left(-4\right)-8=0$

Putting the value in the equation.

  $=>16-8-8=0$

Simplifying the expression.

  $=>16-16=0$

Hence this result is a success.