WEBVTT

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Here is the problem: 1/x plus 1/(2x) equals 3.

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A quadratic equation in x: solve with the quadratic formula.

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Start with the equation.

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Multiply both sides by 2 cdot x ^ 2 to clear the fractions. This is only valid where 2 times x ^ 2 not equal to 0, so any value that makes it zero is excluded at the end.

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Move every term to one side to get standard form.

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Compute the discriminant.

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delta greater than 0, so there are two distinct real roots.

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Apply the quadratic formula.

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Simplify each root.

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Factored form.

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Remove extraneous roots. x equals 0 makes a denominator zero and is rejected.

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So the answer is x equals 1 over 2 approximately 0.5.

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The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

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x equals 0.5: left side equals 3, right side equals 3, which checks out.