Chapter 9.5, Problem 43PPE

To determine

The error in the given solution.

Answer to Problem 43PPE

The error in the first step was to add 25 on both the sides.

Explanation of Solution

Given:

A classmate was completing the square to solve $4x^2+10x=8$ .

She wrote $4x^2+10x+25=8+25$ as her first step.

Calculation:

Solving the given equation:

  $\begin{array}{l}4x^2+10x=8\\ \text{Divide the equation by 4:}\\ {\text{x}}^2+\frac{5}{2}x=2\\ x^2+2.5x=2\\ \text{Add }{\left(\frac{2.5}{2}\right)}^2=1.5625\text{ to both sides:}\\ x^2+2.5x+1.5625=2+1.5625\\ {\left(x+1.25\right)}^2=3.5625\\ x+1.25=\pm \sqrt{3.5625}\\ x+1.25=\pm 1.89\\ x+1.25=1.89\text{ or x + 1}\text{.25 = -1}\text{.89}\\ \text{x = 0}\text{.64 or x = -3}\text{.14}\\ \text{So, x = -3}\text{.14, 0}\text{.64}\end{array}$

Therefore, the error in the first step was to add 25 on both the sides.