Q. 1 - 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 $a^2=49$

Step-by-Step Solution

Answer

The solution of the quadratic equation:

$a=7, a=-7$

Step 1: Given information

Consider the quadratic equation $a^2=49$

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

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

So, $a=\pm \sqrt{49}$

Simplify the radical. 

$$\begin{gathered} a=\pm \sqrt{7·7} \\ a=\pm 7 \end{gathered}$$

Rewrite to show two solutions. 

$a=7, a=-7$

Step 2: Check the solutions

Substitute $a=7$in the original equation.

$$\begin{gathered} a^2=49 \\ {\left(7\right)}^2\stackrel{?}{=}49 \\ 49=49 \end{gathered}$$

Substitute $a=-7$ in the original equation.

$$\begin{gathered} a^2=49 \\ {(-7)}^2\stackrel{?}{=}49 \\ 49=49 \end{gathered}$$