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Simplifying 2(x + -6) = -3x(x + 6) Reorder the terms: 2(-6 + x) = -3x(x + 6) (-6 * 2 + x * 2) = -3x(x + 6) (-12 + 2x) = -3x(x + 6) Reorder the terms: -12 + 2x = -3x(6 + x) -12 + 2x = (6 * -3x + x * -3x) -12 + 2x = (-18x + -3x2) Solving -12 + 2x = -18x + -3x2 Solving for variable 'x'. Combine like terms: 2x + 18x = 20x -12 + 20x + 3x2 = -18x + -3x2 + 18x + 3x2 Reorder the terms: -12 + 20x + 3x2 = -18x + 18x + -3x2 + 3x2 Combine like terms: -18x + 18x = 0 -12 + 20x + 3x2 = 0 + -3x2 + 3x2 -12 + 20x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -12 + 20x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 6.666666667x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 6.666666667x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 6.666666667x + x2 = 0 + 4 6.666666667x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 6.666666667x + x2 = 4 The x term is 6.666666667x. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667x + 11.11111112 + x2 = 4 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x + x2 = 4 + 11.11111112 Combine like terms: 4 + 11.11111112 = 15.11111112 11.11111112 + 6.666666667x + x2 = 15.11111112 Factor a perfect square on the left side: (x + 3.333333334)(x + 3.333333334) = 15.11111112 Calculate the square root of the right side: 3.887301264 Break this problem into two subproblems by setting (x + 3.333333334) equal to 3.887301264 and -3.887301264.Subproblem 1
x + 3.333333334 = 3.887301264 Simplifying x + 3.333333334 = 3.887301264 Reorder the terms: 3.333333334 + x = 3.887301264 Solving 3.333333334 + x = 3.887301264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = 3.887301264 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = 3.887301264 + -3.333333334 x = 3.887301264 + -3.333333334 Combine like terms: 3.887301264 + -3.333333334 = 0.55396793 x = 0.55396793 Simplifying x = 0.55396793Subproblem 2
x + 3.333333334 = -3.887301264 Simplifying x + 3.333333334 = -3.887301264 Reorder the terms: 3.333333334 + x = -3.887301264 Solving 3.333333334 + x = -3.887301264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x = -3.887301264 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x = -3.887301264 + -3.333333334 x = -3.887301264 + -3.333333334 Combine like terms: -3.887301264 + -3.333333334 = -7.220634598 x = -7.220634598 Simplifying x = -7.220634598Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.55396793, -7.220634598}
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