Q.5 - 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 $u^2-300=0$

Step-by-Step Solution

Answer

The solution of the quadratic equation:

$u=10\sqrt{3}, u=-10\sqrt{3}$ 

Step 1. Given information

Consider the quadratic equation $u^2-300=0$

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

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

Isolate the quadratic term and make its coefficient one.  Add 100 to both sides. 

$u^2=300$

Step 2. Apply square root property

So, $u=\pm \sqrt{300}$

Simplify the radical.   

$$\begin{gathered} u=\pm \sqrt{100·3} \\ u=\pm 10\sqrt{3} \end{gathered}$$

Rewrite to show two solutions.  

$u=10\sqrt{3}, u=-10\sqrt{3}$

Step 3. Check the solutions

Substitute $u=10\sqrt{3}$in the original equation.

$$\begin{gathered} u^2-300=0 \\ {\left(10\sqrt{3}\right)}^2-300\stackrel{?}{=}0 \\ 300-300\stackrel{?}{=}0 \\ 0=0 \end{gathered}$$

Substitute $u=-10\sqrt{3}$in the original equation.

$$\begin{gathered} u^2-300=0 \\ {(-10\sqrt{3})}^2-300\stackrel{?}{=}0 \\ 300-300\stackrel{?}{=}0 \\ 0=0 \end{gathered}$$