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:

`√(x^2)=\pm√(25)`
`x=\pm√(25)`

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

`x_1=√(25)`
`x_2=-√(25)`

4. Knowing that:

`√(25)=5`

You get:

`x_1=√(25)=5`
`x_2=-√(25)=-5`

Hence, the answer is:

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