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Published byKristopher Potter Modified over 5 years ago

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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 …

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Example 1: Move all terms to the left side. Solve the equation This equation is now in quadratic form.

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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.

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Solve the quadratic equation.

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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 …

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Solving these two quadratic equations … … we now have the solution to the original equation.

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Example 2: Solve the equation Note that this equation is in quadratic form.

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Use a u-substitution. Let u = expression. The equation now takes the form of a quadratic equation by substituting u for the expression.

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Solve the quadratic equation.

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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 …

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Solving the first equation …

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Solving the second equation …

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The solutions to the original equation are …

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