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Simplifying -7x2 + -1x + 107 = 0 Reorder the terms: 107 + -1x + -7x2 = 0 Solving 107 + -1x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -15.28571429 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '15.28571429' to each side of the equation. -15.28571429 + 0.1428571429x + 15.28571429 + x2 = 0 + 15.28571429 Reorder the terms: -15.28571429 + 15.28571429 + 0.1428571429x + x2 = 0 + 15.28571429 Combine like terms: -15.28571429 + 15.28571429 = 0.00000000 0.00000000 + 0.1428571429x + x2 = 0 + 15.28571429 0.1428571429x + x2 = 0 + 15.28571429 Combine like terms: 0 + 15.28571429 = 15.28571429 0.1428571429x + x2 = 15.28571429 The x term is 0.1428571429x. Take half its coefficient (0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. 0.1428571429x + 0.005102040819 + x2 = 15.28571429 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429x + x2 = 15.28571429 + 0.005102040819 Combine like terms: 15.28571429 + 0.005102040819 = 15.290816330819 0.005102040819 + 0.1428571429x + x2 = 15.290816330819 Factor a perfect square on the left side: (x + 0.07142857145)(x + 0.07142857145) = 15.290816330819 Calculate the square root of the right side: 3.910347341 Break this problem into two subproblems by setting (x + 0.07142857145) equal to 3.910347341 and -3.910347341.Subproblem 1
x + 0.07142857145 = 3.910347341 Simplifying x + 0.07142857145 = 3.910347341 Reorder the terms: 0.07142857145 + x = 3.910347341 Solving 0.07142857145 + x = 3.910347341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = 3.910347341 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = 3.910347341 + -0.07142857145 x = 3.910347341 + -0.07142857145 Combine like terms: 3.910347341 + -0.07142857145 = 3.83891876955 x = 3.83891876955 Simplifying x = 3.83891876955Subproblem 2
x + 0.07142857145 = -3.910347341 Simplifying x + 0.07142857145 = -3.910347341 Reorder the terms: 0.07142857145 + x = -3.910347341 Solving 0.07142857145 + x = -3.910347341 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = -3.910347341 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = -3.910347341 + -0.07142857145 x = -3.910347341 + -0.07142857145 Combine like terms: -3.910347341 + -0.07142857145 = -3.98177591245 x = -3.98177591245 Simplifying x = -3.98177591245Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.83891876955, -3.98177591245}
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