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Simplifying -3x(x + 4) = 2(4x + -6) Reorder the terms: -3x(4 + x) = 2(4x + -6) (4 * -3x + x * -3x) = 2(4x + -6) (-12x + -3x2) = 2(4x + -6) Reorder the terms: -12x + -3x2 = 2(-6 + 4x) -12x + -3x2 = (-6 * 2 + 4x * 2) -12x + -3x2 = (-12 + 8x) Solving -12x + -3x2 = -12 + 8x Solving for variable 'x'. Reorder the terms: 12 + -12x + -8x + -3x2 = -12 + 8x + 12 + -8x Combine like terms: -12x + -8x = -20x 12 + -20x + -3x2 = -12 + 8x + 12 + -8x Reorder the terms: 12 + -20x + -3x2 = -12 + 12 + 8x + -8x Combine like terms: -12 + 12 = 0 12 + -20x + -3x2 = 0 + 8x + -8x 12 + -20x + -3x2 = 8x + -8x Combine like terms: 8x + -8x = 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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