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 ….

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Solving Equations In Quadratic Form

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Solving equations in quadratic form

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 …


Solving equations in quadratic form

  • Example 1:

Solve the equation

Move all terms to the left side.

This equation is now in quadratic form.


Solving equations 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.


Solving equations in quadratic form

Solve the quadratic equation.


Solving equations in quadratic form

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 equations in quadratic form

Solving these two quadratic equations …

… we now have the solution to the original equation.


Solving equations in quadratic form

  • Example 2:

Solve the equation

Note that this equation is in quadratic form.


Solving equations 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.


Solving equations in quadratic form

Solve the quadratic equation.


Solving equations in quadratic form

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 equations in quadratic form

Solving the first equation …


Solving equations in quadratic form

Solving the second equation …


Solving equations in quadratic form

The solutions to the original equation are …


Solving equations in quadratic form

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