Q.2 - Intermediate Algebra

Question

Solve Quadratic Equations of the Form $a{x}^2=k$Using the Square Root Property.

In the following exercises, solve each equation $b^2=144$

Step-by-Step Solution

Answer

The solution of the quadratic equation: 

$b=12, b=-12$

Step 1. Given information

Consider the quadratic equation  $b^2=144$

The objective is to solve the quadratic equation by using the square root property.

If $x^2=k$, then $x=\pm \sqrt{k}$

So, $b=\pm \sqrt{144}$

Simplify the radical.  

$$\begin{gathered} b=\pm \sqrt{12·12} \\ b=\pm 12 \end{gathered}$$

Rewrite to show two solutions. 

$b=12, b=-12$

Step 2. Check the solutions

Substitute $b=12$ in the original equation

$$\begin{gathered} b^2=144 \\ {\left(12\right)}^2\stackrel{?}{=}144 \\ 144=144 \end{gathered}$$

Substitute $b=-12$in the original equation.

$$\begin{gathered} b^2=144 \\ {(-12)}^2\stackrel{?}{=}144 \\ 144=144 \end{gathered}$$