Chapter SH, Problem 4.7EP

To determine

Find the solution of the given equation using factorization method.

Answer to Problem 4.7EP

The solutions of the given equation are $x=-4\text{and}x=\frac{7}{2}$ .

Explanation of Solution

Given:

The given equation is $2x^2+x=28$ .

Calculation:

  $2x^2+x=28$

Subtract $28$ from both sides.

  $\begin{array}{l}\Rightarrow 2x^2+x-28=28-28\\ \Rightarrow 2x^2+x-28=0\end{array}$

Use factorization method.

  $\begin{array}{l}\Rightarrow 2x^2+8x-7x-28=0\\ \Rightarrow 2x\left(x+4\right)-7\left(x+4\right)=0\\ \Rightarrow \left(x+4\right)\left(2x-7\right)=0\\ \Rightarrow x+4=0\text{and}2x-7=0\\ \Rightarrow x+4-4=0-4\text{and}2x-7+7=0+7\\ \Rightarrow x=-4\text{and}2x=7\\ \Rightarrow x=-4\text{and}\frac{2}{2}x=\frac{7}{2}\\ \Rightarrow x=-4\text{and}x=\frac{7}{2}\end{array}$

Hence the solutions of the given equation are $x=-4\text{and}x=\frac{7}{2}$ .