# Solve equations that are quadratic in form by substitution to create a quadratic equation

We have seen three different ways to solve quadratics: factoring, completing the square, and the quadratic formula. A quadratic is any equation of the form , however, we can use the skills learned to solve quadratics to solve problems with higher (or sometimes lower) powers if the equation is in what is called quadratic form.

Quadratic form: where *m = 2n.*

An equation is in quadratic form if one of the exponents on a variable is double the exponent on the same variable somewhere else in the equation. If this is the case we can create a new variable, set it equal to the variable with smallest exponent. When we substitute this into the equation we will have a quadratic equation we can solve.

Also Read:

**Also Read : Solve revenue and distance applications of quadratic equations**

**World View Note: **Arab mathematicians around the year 1000 were the first to use this method!.

**Example:**

Solve the solution

Solution:

Quadratic form, one exponent, 4, double the other, 2

New variable equal to the variable with smaller exponent

Substitute y for x^{2 }and y^{2} for x^{4 }.

Solve. We can solve this equation by factoring

(y – 9)(y – 4) = 0

Set each factor equal to zero

y – 9 = 0 or y – 4 = 0

y = 9 or y = 4

Substitute values for y

or

or

or

Our solution is .