WEBVTT

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Here is the problem: 3x squared minus 7x minus 3 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 (7 minus the square root of 85 over 6 approximately negative 0.36992408 or x equals (7 plus the square root of 85 over 6 approximately 2.7032574.

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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 0.36992408: left side equals 0, right side equals 0, which checks out.

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x equals 2.7032574: left side equals 0, right side equals 0, which checks out.