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Solving Equations In Quadratic Form

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Solving Equations In Quadratic Form

- There are several methods one can use to solve a quadratic equation. Sometimes we are called upon to solve an equation that is in Quadratic Form.

- A quadratic equation is an equation that can be simplified into the form …

- An equation in quadratic form can be simplified into the form …

- Example 1:

Solve the equation

Move all terms to the left side.

This equation is now in quadratic form.

We will solve the equation with what is called a

u-substitution. Let u = expression.

The equation now takes the form of a quadratic equation by substituting u for the expression.

Solve the quadratic equation.

Since the original equation was in variable x, our solutions need to be in variable x. Taking the solutions of u and combining them with the original

u-substitution equation we get …

Solving these two quadratic equations …

… we now have the solution to the original equation.

- Example 2:

Solve the equation

Note that this equation is in quadratic form.

Use a u-substitution. Let u = expression.

The equation now takes the form of a quadratic equation by substituting u for the expression.

Solve the quadratic equation.

Since the original equation was in variable x, our solutions need to be in variable x. Taking the solutions of u and combining them with the original

u-substitution equation we get …

Solving the first equation …

Solving the second equation …

The solutions to the original equation are …

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