Question

Solve by using square roots x^(2)-14=11

Answer 1

Given the Quadratic Equation:

$x^2-14=11$

You can solve it as follows:

1. Apply the Addition Property of Equality by adding 14 to both sides of the equation:

$x^2-14+\((14)\)=11+(14)$$x^2=25$

2. By definition, the square root undoes the effect of exponent 2 on the variable. Then, you have to take the square root of both sides of the equation:

$\sqrt{x^2}=\pm\sqrt{25}$$x=\pm\sqrt{25}$

3. Notice that you can split the equations into two equations:

$x_1=\sqrt{25}$$x_2=-\sqrt{25}$

4. Knowing that:

$\sqrt{25}=5$

You get:

$x_1=\sqrt{25}=5$$x_2=-\sqrt{25}=-5$

Hence, the answer is:

$\begin{gathered} x_1=5 \\ x_2=-5 \end{gathered}$