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Simplifying 12x2 + 47x + -88 = 0 Reorder the terms: -88 + 47x + 12x2 = 0 Solving -88 + 47x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -7.333333333 + 3.916666667x + x2 = 0 Move the constant term to the right: Add '7.333333333' to each side of the equation. -7.333333333 + 3.916666667x + 7.333333333 + x2 = 0 + 7.333333333 Reorder the terms: -7.333333333 + 7.333333333 + 3.916666667x + x2 = 0 + 7.333333333 Combine like terms: -7.333333333 + 7.333333333 = 0.000000000 0.000000000 + 3.916666667x + x2 = 0 + 7.333333333 3.916666667x + x2 = 0 + 7.333333333 Combine like terms: 0 + 7.333333333 = 7.333333333 3.916666667x + x2 = 7.333333333 The x term is 3.916666667x. Take half its coefficient (1.958333334). Square it (3.835069447) and add it to both sides. Add '3.835069447' to each side of the equation. 3.916666667x + 3.835069447 + x2 = 7.333333333 + 3.835069447 Reorder the terms: 3.835069447 + 3.916666667x + x2 = 7.333333333 + 3.835069447 Combine like terms: 7.333333333 + 3.835069447 = 11.16840278 3.835069447 + 3.916666667x + x2 = 11.16840278 Factor a perfect square on the left side: (x + 1.958333334)(x + 1.958333334) = 11.16840278 Calculate the square root of the right side: 3.341916034 Break this problem into two subproblems by setting (x + 1.958333334) equal to 3.341916034 and -3.341916034.Subproblem 1
x + 1.958333334 = 3.341916034 Simplifying x + 1.958333334 = 3.341916034 Reorder the terms: 1.958333334 + x = 3.341916034 Solving 1.958333334 + x = 3.341916034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.958333334' to each side of the equation. 1.958333334 + -1.958333334 + x = 3.341916034 + -1.958333334 Combine like terms: 1.958333334 + -1.958333334 = 0.000000000 0.000000000 + x = 3.341916034 + -1.958333334 x = 3.341916034 + -1.958333334 Combine like terms: 3.341916034 + -1.958333334 = 1.3835827 x = 1.3835827 Simplifying x = 1.3835827Subproblem 2
x + 1.958333334 = -3.341916034 Simplifying x + 1.958333334 = -3.341916034 Reorder the terms: 1.958333334 + x = -3.341916034 Solving 1.958333334 + x = -3.341916034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.958333334' to each side of the equation. 1.958333334 + -1.958333334 + x = -3.341916034 + -1.958333334 Combine like terms: 1.958333334 + -1.958333334 = 0.000000000 0.000000000 + x = -3.341916034 + -1.958333334 x = -3.341916034 + -1.958333334 Combine like terms: -3.341916034 + -1.958333334 = -5.300249368 x = -5.300249368 Simplifying x = -5.300249368Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3835827, -5.300249368}
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