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Simplifying 9x2 + 131x + -10 = 0 Reorder the terms: -10 + 131x + 9x2 = 0 Solving -10 + 131x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + 14.55555556x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + 14.55555556x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + 14.55555556x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + 14.55555556x + x2 = 0 + 1.111111111 14.55555556x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 14.55555556x + x2 = 1.111111111 The x term is 14.55555556x. Take half its coefficient (7.27777778). Square it (52.96604942) and add it to both sides. Add '52.96604942' to each side of the equation. 14.55555556x + 52.96604942 + x2 = 1.111111111 + 52.96604942 Reorder the terms: 52.96604942 + 14.55555556x + x2 = 1.111111111 + 52.96604942 Combine like terms: 1.111111111 + 52.96604942 = 54.077160531 52.96604942 + 14.55555556x + x2 = 54.077160531 Factor a perfect square on the left side: (x + 7.27777778)(x + 7.27777778) = 54.077160531 Calculate the square root of the right side: 7.353717463 Break this problem into two subproblems by setting (x + 7.27777778) equal to 7.353717463 and -7.353717463.Subproblem 1
x + 7.27777778 = 7.353717463 Simplifying x + 7.27777778 = 7.353717463 Reorder the terms: 7.27777778 + x = 7.353717463 Solving 7.27777778 + x = 7.353717463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.27777778' to each side of the equation. 7.27777778 + -7.27777778 + x = 7.353717463 + -7.27777778 Combine like terms: 7.27777778 + -7.27777778 = 0.00000000 0.00000000 + x = 7.353717463 + -7.27777778 x = 7.353717463 + -7.27777778 Combine like terms: 7.353717463 + -7.27777778 = 0.075939683 x = 0.075939683 Simplifying x = 0.075939683Subproblem 2
x + 7.27777778 = -7.353717463 Simplifying x + 7.27777778 = -7.353717463 Reorder the terms: 7.27777778 + x = -7.353717463 Solving 7.27777778 + x = -7.353717463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.27777778' to each side of the equation. 7.27777778 + -7.27777778 + x = -7.353717463 + -7.27777778 Combine like terms: 7.27777778 + -7.27777778 = 0.00000000 0.00000000 + x = -7.353717463 + -7.27777778 x = -7.353717463 + -7.27777778 Combine like terms: -7.353717463 + -7.27777778 = -14.631495243 x = -14.631495243 Simplifying x = -14.631495243Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.075939683, -14.631495243}
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