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.