WEBVTT

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Here is the problem: x squared minus 13x plus 42 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 each root.

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Factored form.

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Now look at the graph of the left side minus the right side.

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It crosses zero exactly at the solutions we found.

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So the answer is x equals 6 or x equals 7.

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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 6: left side equals 0, right side equals 0, which checks out.

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x equals 7: left side equals 0, right side equals 0, which checks out.