Chapter 1.5, Problem 52E

To determine

Solve the equations by factoring.

Answer to Problem 52E

  $x=3,-3$

Explanation of Solution

Given information:

  $3x^2-27=0$

Formula used:

Splitting the middle term:- in this method, middle term is splitted in such a way that the product of its part is equal to the product of constant and first terms coefficient.

Calculation:

  $\begin{array}{l}3x^2-27=0\\ 3x^2+0x-27=0\end{array}$

Splitting middle term in such a way that product of its part is equal to product of constant and coefficient of first term.

  $\begin{array}{l}3x^2+0x-27=0\\ 3x^2-9x+9x-27=0\\ 3x\left(x-3\right)+9\left(x-3\right)=0\\ \left(x-3\right)\left(3x+9\right)=0\end{array}$

  $\begin{array}{l}x=3,\frac{-9}{3}\\ \boxed{x=3,-3}\end{array}$