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Simplifying (4x2 + -2x + -58) + (3x2 + 3x) = 0 Reorder the terms: (-58 + -2x + 4x2) + (3x2 + 3x) = 0 Remove parenthesis around (-58 + -2x + 4x2) -58 + -2x + 4x2 + (3x2 + 3x) = 0 Reorder the terms: -58 + -2x + 4x2 + (3x + 3x2) = 0 Remove parenthesis around (3x + 3x2) -58 + -2x + 4x2 + 3x + 3x2 = 0 Reorder the terms: -58 + -2x + 3x + 4x2 + 3x2 = 0 Combine like terms: -2x + 3x = 1x -58 + 1x + 4x2 + 3x2 = 0 Combine like terms: 4x2 + 3x2 = 7x2 -58 + 1x + 7x2 = 0 Solving -58 + 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'. -8.285714286 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '8.285714286' to each side of the equation. -8.285714286 + 0.1428571429x + 8.285714286 + x2 = 0 + 8.285714286 Reorder the terms: -8.285714286 + 8.285714286 + 0.1428571429x + x2 = 0 + 8.285714286 Combine like terms: -8.285714286 + 8.285714286 = 0.000000000 0.000000000 + 0.1428571429x + x2 = 0 + 8.285714286 0.1428571429x + x2 = 0 + 8.285714286 Combine like terms: 0 + 8.285714286 = 8.285714286 0.1428571429x + x2 = 8.285714286 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 = 8.285714286 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429x + x2 = 8.285714286 + 0.005102040819 Combine like terms: 8.285714286 + 0.005102040819 = 8.290816326819 0.005102040819 + 0.1428571429x + x2 = 8.290816326819 Factor a perfect square on the left side: (x + 0.07142857145)(x + 0.07142857145) = 8.290816326819 Calculate the square root of the right side: 2.879377767 Break this problem into two subproblems by setting (x + 0.07142857145) equal to 2.879377767 and -2.879377767.Subproblem 1
x + 0.07142857145 = 2.879377767 Simplifying x + 0.07142857145 = 2.879377767 Reorder the terms: 0.07142857145 + x = 2.879377767 Solving 0.07142857145 + x = 2.879377767 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 = 2.879377767 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = 2.879377767 + -0.07142857145 x = 2.879377767 + -0.07142857145 Combine like terms: 2.879377767 + -0.07142857145 = 2.80794919555 x = 2.80794919555 Simplifying x = 2.80794919555Subproblem 2
x + 0.07142857145 = -2.879377767 Simplifying x + 0.07142857145 = -2.879377767 Reorder the terms: 0.07142857145 + x = -2.879377767 Solving 0.07142857145 + x = -2.879377767 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 = -2.879377767 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = -2.879377767 + -0.07142857145 x = -2.879377767 + -0.07142857145 Combine like terms: -2.879377767 + -0.07142857145 = -2.95080633845 x = -2.95080633845 Simplifying x = -2.95080633845Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.80794919555, -2.95080633845}
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