WEBVTT

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Here is the problem: |x squared minus 5x| equals 6.

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Solve for x numerically (the equation contains functions such as sin, log or roots).

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Start with the equation.

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Rewrite as f(x) equals 0.

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This equation is not polynomial, so solve it numerically. Scan x from negative 10 to the power 9 to 10 to the power 9 for sign changes of f and for points where the graph touches the axis, then narrow each one down. Every root is checked by substituting it back.

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Found 4 solutions in [−10 to the power 9, 10 to the power 9].

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So the answer is x equals negative 1, x equals 2, x equals 3, x equals 6.

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Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

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x equals negative 1: left side equals 6, right side equals 6, which checks out.

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x equals 2: left side equals 6, right side equals 6, which checks out.

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x equals 3: left side equals 6, right side equals 6, which checks out.

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