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Simplifying -3x2 + 11x + 12 = 0 Reorder the terms: 12 + 11x + -3x2 = 0 Solving 12 + 11x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -4 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -3.666666667x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -3.666666667x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3.666666667x + x2 = 0 + 4 -3.666666667x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -3.666666667x + x2 = 4 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = 4 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 4 + 3.361111114 Combine like terms: 4 + 3.361111114 = 7.361111114 3.361111114 + -3.666666667x + x2 = 7.361111114 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 7.361111114 Calculate the square root of the right side: 2.713136767 Break this problem into two subproblems by setting (x + -1.833333334) equal to 2.713136767 and -2.713136767.Subproblem 1
x + -1.833333334 = 2.713136767 Simplifying x + -1.833333334 = 2.713136767 Reorder the terms: -1.833333334 + x = 2.713136767 Solving -1.833333334 + x = 2.713136767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 2.713136767 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 2.713136767 + 1.833333334 x = 2.713136767 + 1.833333334 Combine like terms: 2.713136767 + 1.833333334 = 4.546470101 x = 4.546470101 Simplifying x = 4.546470101Subproblem 2
x + -1.833333334 = -2.713136767 Simplifying x + -1.833333334 = -2.713136767 Reorder the terms: -1.833333334 + x = -2.713136767 Solving -1.833333334 + x = -2.713136767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -2.713136767 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -2.713136767 + 1.833333334 x = -2.713136767 + 1.833333334 Combine like terms: -2.713136767 + 1.833333334 = -0.879803433 x = -0.879803433 Simplifying x = -0.879803433Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.546470101, -0.879803433}
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