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Simplifying 2x * x + 2x + 3 = 132 Multiply x * x 2x2 + 2x + 3 = 132 Reorder the terms: 3 + 2x + 2x2 = 132 Solving 3 + 2x + 2x2 = 132 Solving for variable 'x'. Reorder the terms: 3 + -132 + 2x + 2x2 = 132 + -132 Combine like terms: 3 + -132 = -129 -129 + 2x + 2x2 = 132 + -132 Combine like terms: 132 + -132 = 0 -129 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -64.5 + x + x2 = 0 Move the constant term to the right: Add '64.5' to each side of the equation. -64.5 + x + 64.5 + x2 = 0 + 64.5 Reorder the terms: -64.5 + 64.5 + x + x2 = 0 + 64.5 Combine like terms: -64.5 + 64.5 = 0.0 0.0 + x + x2 = 0 + 64.5 x + x2 = 0 + 64.5 Combine like terms: 0 + 64.5 = 64.5 x + x2 = 64.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 64.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 64.5 + 0.25 Combine like terms: 64.5 + 0.25 = 64.75 1.25 + x2 = 64.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 64.75 Calculate the square root of the right side: 8.04673847 Break this problem into two subproblems by setting (x + 0.5) equal to 8.04673847 and -8.04673847.Subproblem 1
x + 0.5 = 8.04673847 Simplifying x + 0.5 = 8.04673847 Reorder the terms: 0.5 + x = 8.04673847 Solving 0.5 + x = 8.04673847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 8.04673847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.04673847 + -0.5 x = 8.04673847 + -0.5 Combine like terms: 8.04673847 + -0.5 = 7.54673847 x = 7.54673847 Simplifying x = 7.54673847Subproblem 2
x + 0.5 = -8.04673847 Simplifying x + 0.5 = -8.04673847 Reorder the terms: 0.5 + x = -8.04673847 Solving 0.5 + x = -8.04673847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -8.04673847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.04673847 + -0.5 x = -8.04673847 + -0.5 Combine like terms: -8.04673847 + -0.5 = -8.54673847 x = -8.54673847 Simplifying x = -8.54673847Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.54673847, -8.54673847}
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