Chapter 4.4, Problem 77E

To determine

To solve: the given quadratic equation by factorization.

Answer to Problem 77E

The solution of the given equation is $x=6,x=-5$ .

Explanation of Solution

Given information:

A quadratic equation is given as

  $x^2-x-30=0$

Calculation:

Consider the given equation.

  $x^2-x-30=0$

Now, break the coefficient of middle term $-1$ 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 $-30$ .

Such numbers will be $-6$ and $5$ .

Now, factorize left side of $x^2-x-30=0$ as shown:

  $\begin{array}{c}{x}^2-x-30=0\\ x^2-6x+5x-30=0\\ x\left(x-6\right)+5\left(x-6\right)=0\\ \left(x-6\right)\left(x+5\right)=0\end{array}$

Solution can be found by equating each factor with 0.

  $\begin{array}{c}x-6=0\\ x=6\end{array}$ and $\begin{array}{c}x+5=0\\ x=-5\end{array}$

Therefore, the solution of the given equation is $x=6,x=-5$ .