Chapter 4.3, Problem 52PPS

To determine

To calculate: The solution of the equation $75x^2-60x=-12$ by factoring.

Answer to Problem 52PPS

The solution of the equation is $\frac{2}{5}$ .

Explanation of Solution

Given information:

The equation $75x^2-60x=-12$ .

Formula used:

Solution of a polynomial equation is calculated using middle term splitting method and then common factors are taken out and simplified.

Calculation:

Consider the given equation $75x^2-60x=-12$ .

Recall that solution of a polynomial equation is calculated using middle term splitting method and then common factors are taken out and simplified.

So, $75x^2-60x=-12$ will be factorized as,

  $\begin{array}{c}75x^2-60x=-12\\ 75x^2-60x+12=0\\ 25x^2-20x+4=0\\ {\left(5x-2\right)}^2=0\end{array}$ .

Therefore,

  $\begin{array}{c}{\left(5x-2\right)}^2=0\\ 5x-2=0\\ x=\frac{2}{5}\end{array}$ .

Thus, the solution of the equation is $\frac{2}{5}$ .