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Simplifying (5x2 + -4x + 12) + (6x2 + 9x + -86) = 0 Reorder the terms: (12 + -4x + 5x2) + (6x2 + 9x + -86) = 0 Remove parenthesis around (12 + -4x + 5x2) 12 + -4x + 5x2 + (6x2 + 9x + -86) = 0 Reorder the terms: 12 + -4x + 5x2 + (-86 + 9x + 6x2) = 0 Remove parenthesis around (-86 + 9x + 6x2) 12 + -4x + 5x2 + -86 + 9x + 6x2 = 0 Reorder the terms: 12 + -86 + -4x + 9x + 5x2 + 6x2 = 0 Combine like terms: 12 + -86 = -74 -74 + -4x + 9x + 5x2 + 6x2 = 0 Combine like terms: -4x + 9x = 5x -74 + 5x + 5x2 + 6x2 = 0 Combine like terms: 5x2 + 6x2 = 11x2 -74 + 5x + 11x2 = 0 Solving -74 + 5x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -6.727272727 + 0.4545454545x + x2 = 0 Move the constant term to the right: Add '6.727272727' to each side of the equation. -6.727272727 + 0.4545454545x + 6.727272727 + x2 = 0 + 6.727272727 Reorder the terms: -6.727272727 + 6.727272727 + 0.4545454545x + x2 = 0 + 6.727272727 Combine like terms: -6.727272727 + 6.727272727 = 0.000000000 0.000000000 + 0.4545454545x + x2 = 0 + 6.727272727 0.4545454545x + x2 = 0 + 6.727272727 Combine like terms: 0 + 6.727272727 = 6.727272727 0.4545454545x + x2 = 6.727272727 The x term is 0.4545454545x. Take half its coefficient (0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. 0.4545454545x + 0.05165289257 + x2 = 6.727272727 + 0.05165289257 Reorder the terms: 0.05165289257 + 0.4545454545x + x2 = 6.727272727 + 0.05165289257 Combine like terms: 6.727272727 + 0.05165289257 = 6.77892561957 0.05165289257 + 0.4545454545x + x2 = 6.77892561957 Factor a perfect square on the left side: (x + 0.2272727273)(x + 0.2272727273) = 6.77892561957 Calculate the square root of the right side: 2.603636998 Break this problem into two subproblems by setting (x + 0.2272727273) equal to 2.603636998 and -2.603636998.Subproblem 1
x + 0.2272727273 = 2.603636998 Simplifying x + 0.2272727273 = 2.603636998 Reorder the terms: 0.2272727273 + x = 2.603636998 Solving 0.2272727273 + x = 2.603636998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = 2.603636998 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = 2.603636998 + -0.2272727273 x = 2.603636998 + -0.2272727273 Combine like terms: 2.603636998 + -0.2272727273 = 2.3763642707 x = 2.3763642707 Simplifying x = 2.3763642707Subproblem 2
x + 0.2272727273 = -2.603636998 Simplifying x + 0.2272727273 = -2.603636998 Reorder the terms: 0.2272727273 + x = -2.603636998 Solving 0.2272727273 + x = -2.603636998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = -2.603636998 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = -2.603636998 + -0.2272727273 x = -2.603636998 + -0.2272727273 Combine like terms: -2.603636998 + -0.2272727273 = -2.8309097253 x = -2.8309097253 Simplifying x = -2.8309097253Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3763642707, -2.8309097253}
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