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Simplifying 132 = (x + 7) * 2 + x2 Reorder the terms: 132 = (7 + x) * 2 + x2 Reorder the terms for easier multiplication: 132 = 2(7 + x) + x2 132 = (7 * 2 + x * 2) + x2 132 = (14 + 2x) + x2 Solving 132 = 14 + 2x + x2 Solving for variable 'x'. Combine like terms: 132 + -14 = 118 118 + -2x + -1x2 = 14 + 2x + x2 + -14 + -2x + -1x2 Reorder the terms: 118 + -2x + -1x2 = 14 + -14 + 2x + -2x + x2 + -1x2 Combine like terms: 14 + -14 = 0 118 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 118 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 118 + -2x + -1x2 = 0 + x2 + -1x2 118 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 118 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -118 + 2x + x2 = 0 Move the constant term to the right: Add '118' to each side of the equation. -118 + 2x + 118 + x2 = 0 + 118 Reorder the terms: -118 + 118 + 2x + x2 = 0 + 118 Combine like terms: -118 + 118 = 0 0 + 2x + x2 = 0 + 118 2x + x2 = 0 + 118 Combine like terms: 0 + 118 = 118 2x + x2 = 118 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 118 + 1 Reorder the terms: 1 + 2x + x2 = 118 + 1 Combine like terms: 118 + 1 = 119 1 + 2x + x2 = 119 Factor a perfect square on the left side: (x + 1)(x + 1) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (x + 1) equal to 10.908712115 and -10.908712115.Subproblem 1
x + 1 = 10.908712115 Simplifying x + 1 = 10.908712115 Reorder the terms: 1 + x = 10.908712115 Solving 1 + x = 10.908712115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 10.908712115 + -1 Combine like terms: 1 + -1 = 0 0 + x = 10.908712115 + -1 x = 10.908712115 + -1 Combine like terms: 10.908712115 + -1 = 9.908712115 x = 9.908712115 Simplifying x = 9.908712115Subproblem 2
x + 1 = -10.908712115 Simplifying x + 1 = -10.908712115 Reorder the terms: 1 + x = -10.908712115 Solving 1 + x = -10.908712115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -10.908712115 + -1 Combine like terms: 1 + -1 = 0 0 + x = -10.908712115 + -1 x = -10.908712115 + -1 Combine like terms: -10.908712115 + -1 = -11.908712115 x = -11.908712115 Simplifying x = -11.908712115Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.908712115, -11.908712115}
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