WEBVTT

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Here is the problem: negative 7x squared plus 13x minus 31 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 less than 0, so there are no real roots; the two roots are complex conjugates.

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Apply the quadratic formula with the square root of negative 1 equals i.

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Simplify.

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So the answer is x equals (13 minus the square root of 699 times i/14 or x equals (13 plus the square root of 699 times i/14.

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The discriminant is negative, so there are no real solutions; the solutions are a pair of complex conjugates.

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Vieta: sum of roots equals 1.8571429 equals negative b/a equals 1.8571429; product equals 4.4285714 equals c/a equals 4.4285714.