Q 290 - Intermediate Algebra

Question

In the following exercises, solve:

$625=x^2$

Step-by-Step Solution

Answer

On solving the equation, we get $x=25,-25$.

Step 1. Given information.

Consider the given equation,

$625=x^2$

Write the quadratic equation in standard form,

$625-x^2=0$

Step 2. Factor the quadratic expression.

On factoring, we get,

$$\begin{gathered} x^2-{\left(25\right)}^2=0 \\ \left(x-25\right)\left(x+25\right)=0 \end{gathered}$$

Use the zero product property,

$$\begin{gathered} x-25=0 \\ x=25 \end{gathered}$$

Then,

$$\begin{gathered} x+25=0 \\ x=-25 \end{gathered}$$

Step 3. Check the answers.

Substitute $x=25$ in the given equation,

$$\begin{gathered} 625={\left(25\right)}^2 \\ 625=625 \end{gathered}$$

This is true.

Substitute $x=-25$ in the given equation,

$$\begin{gathered} 625={\left(-25\right)}^2 \\ 625=625 \end{gathered}$$

This is also true.

Hence, the answer is $x=25,-25$.