# Quadratic Equation: Square Root

How to solve a quadratic equation by square rooting both sides: 3 examples and their solutions.

## Examplex^{2} = 9

A quadratic equation is an equation

that has a quadratic term: x^{2}.

Solution

Solution (Detail)

See the given equation

x^{2} = 9.

The left side is x^{2}.

The right side is plus.

Then square root both sides.

The left side is x.

The right side is

plus minus

square root

9.

±√9 = ±√3^{2} = ±3

Square Root

So x = ±3.

## Examplex^{2} - 7 = 0

Solution

Solution (Detail)

Move -7 to the right side.

The left side is x^{2}.

The right side is plus.

Then square root both sides.

The left side is x.

The right side is

plus minus

square root

7.

So x = ±√7.

## Examplex^{2} = -2

Solution

Solution (Detail)

The left side is x^{2}.

It's either 0 or plus.

But the right side is minus.

Then this quadratic equation has no solution.

So

no solution

is the answer.