Chapter 8, Problem 1RE

In Exercises 1–5, solve each equation by the square root property. If possible, simplify radicals or rationalize denominators. Express imaginary solutions in the form $a+bi.$

$2x^2-3=125$

To determine

To calculate: The solution of equation $2x^2-3=125$ by square root property.

Answer to Problem 1RE

Solution:

The solution of equation $2x^2-3=125$ is $\left\{-8,8\right\}$.

Explanation of Solution

Given:

The equation is $2x^2-3=125$.

Formula used:

The square root property is:

$\begin{array}{c}{u}^2=d\\ u=\pm \sqrt{d}\end{array}$

Calculation:

The provided equation is:

$2x^2-3=125$

Add 3 to the both sides of equation as:

$\begin{array}{c}2x^2-3+3=125+3\\ 2x^2=128\end{array}$

Divide it further by 2 as:

$x^2=64$

By applying square root property:

$\begin{array}{c}x=\pm \sqrt{64}\\ x=\pm 8\end{array}$

There is dual sign as the same number having positive or negative sign will yield the same square.

Hence, the solution of equation $2x^2-3=125$ is $\left\{-8,8\right\}$.