Quadratic Equation: Square Root

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

Example 1

Example

A quadratic equation is an equation
that has a quadratic term: x².

Solution

See the given equation
x² = 9.

The left side is x².
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 = ±√3² = ±3

Square Root

So x = ±3.

Example 2

Example

Solution

Move -7 to the right side.

The left side is x².
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.

Example 3

Example

Solution

The left side is x².
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.