Chapter 4.4, Problem 78E

To determine

To solve: the given quadratic equation by factorization.

Answer to Problem 78E

The solution of the given equation is $x=9,x=-4$ .

Explanation of Solution

Given information:

A quadratic equation is given as

  $2x^2-10x-72=0$

Calculation:

Consider the given equation.

  $\begin{array}{c}2x^2-10x-72=0\\ 2\left(x^2-5x-36\right)=0\end{array}$

Now, break the coefficient of middle term $-5$ as sum or difference of two numbers such that product of the numbers is equal to the product of first term and constant term that is product of $1$ and $-36$ .

Such numbers will be $-9$ and $4$ .

Now, factorize left side of $x^2-5x-36=0$ as shown:

  $\begin{array}{c}{x}^2-5x-36=0\\ x^2-9x+4x-36=0\\ x\left(x-9\right)+4\left(x-9\right)=0\\ \left(x-9\right)\left(x+4\right)=0\end{array}$

Solution can be found by equating each factor with 0.

  $\begin{array}{c}x-9=0\\ x=9\end{array}$ and $\begin{array}{c}x+4=0\\ x=-4\end{array}$

Therefore, the solution of the given equation is $x=9,x=-4$ .