Chapter 4.3, Problem 61PPS

To determine

To calculate: The solution of the equation $x^2+0.25x=1.25$ by factoring.

Answer to Problem 61PPS

The solution of the equation is $1\text{ and }\frac{-5}{4}$ .

Explanation of Solution

Given information:

The equation $x^2+0.25x=1.25$ .

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 $x^2+0.25x=1.25$ .

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

So, $x^2+0.25x=1.25$ will be factorized as,

  $\begin{array}{c}{x}^2+0.25x=1.25\\ x^2+\frac{1}{4}x-\frac{5}{4}=0\\ 4x^2+x-5=0\\ \left(x-1\right)\left(4x+5\right)=0\end{array}$ .

Therefore, either $\begin{array}{c}x-1=0\text{ or }4x+5=0\\ x=1\text{ or }x=\frac{-5}{4}\end{array}$ .

Thus, the solution of the equation is $1\text{ and }\frac{-5}{4}$ .