WEBVTT

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Here is the problem: x squared minus 2x minus 1 equals 0.

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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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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 the square root.

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Reduce the fraction.

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So the answer is x equals 1 minus the square root of 2 approximately negative 0.41421356 or x equals 1 plus the square root of 2 approximately 2.4142136.

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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 negative 0.41421356: left side equals 0, right side equals 0, which checks out.

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x equals 2.4142136: left side equals 0, right side equals 0, which checks out.