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Simplifying -3x(x + -16) = 12 + -1x Reorder the terms: -3x(-16 + x) = 12 + -1x (-16 * -3x + x * -3x) = 12 + -1x (48x + -3x2) = 12 + -1x Solving 48x + -3x2 = 12 + -1x Solving for variable 'x'. Reorder the terms: -12 + 48x + x + -3x2 = 12 + -1x + -12 + x Combine like terms: 48x + x = 49x -12 + 49x + -3x2 = 12 + -1x + -12 + x Reorder the terms: -12 + 49x + -3x2 = 12 + -12 + -1x + x Combine like terms: 12 + -12 = 0 -12 + 49x + -3x2 = 0 + -1x + x -12 + 49x + -3x2 = -1x + x Combine like terms: -1x + x = 0 -12 + 49x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 4 + -16.33333333x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -16.33333333x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -16.33333333x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -16.33333333x + x2 = 0 + -4 -16.33333333x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -16.33333333x + x2 = -4 The x term is -16.33333333x. Take half its coefficient (-8.166666665). Square it (66.69444442) and add it to both sides. Add '66.69444442' to each side of the equation. -16.33333333x + 66.69444442 + x2 = -4 + 66.69444442 Reorder the terms: 66.69444442 + -16.33333333x + x2 = -4 + 66.69444442 Combine like terms: -4 + 66.69444442 = 62.69444442 66.69444442 + -16.33333333x + x2 = 62.69444442 Factor a perfect square on the left side: (x + -8.166666665)(x + -8.166666665) = 62.69444442 Calculate the square root of the right side: 7.917982345 Break this problem into two subproblems by setting (x + -8.166666665) equal to 7.917982345 and -7.917982345.Subproblem 1
x + -8.166666665 = 7.917982345 Simplifying x + -8.166666665 = 7.917982345 Reorder the terms: -8.166666665 + x = 7.917982345 Solving -8.166666665 + x = 7.917982345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.166666665' to each side of the equation. -8.166666665 + 8.166666665 + x = 7.917982345 + 8.166666665 Combine like terms: -8.166666665 + 8.166666665 = 0.000000000 0.000000000 + x = 7.917982345 + 8.166666665 x = 7.917982345 + 8.166666665 Combine like terms: 7.917982345 + 8.166666665 = 16.08464901 x = 16.08464901 Simplifying x = 16.08464901Subproblem 2
x + -8.166666665 = -7.917982345 Simplifying x + -8.166666665 = -7.917982345 Reorder the terms: -8.166666665 + x = -7.917982345 Solving -8.166666665 + x = -7.917982345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.166666665' to each side of the equation. -8.166666665 + 8.166666665 + x = -7.917982345 + 8.166666665 Combine like terms: -8.166666665 + 8.166666665 = 0.000000000 0.000000000 + x = -7.917982345 + 8.166666665 x = -7.917982345 + 8.166666665 Combine like terms: -7.917982345 + 8.166666665 = 0.24868432 x = 0.24868432 Simplifying x = 0.24868432Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.08464901, 0.24868432}
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