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Simplifying 2x * x + 3x + 3 = 132 Multiply x * x 2x2 + 3x + 3 = 132 Reorder the terms: 3 + 3x + 2x2 = 132 Solving 3 + 3x + 2x2 = 132 Solving for variable 'x'. Reorder the terms: 3 + -132 + 3x + 2x2 = 132 + -132 Combine like terms: 3 + -132 = -129 -129 + 3x + 2x2 = 132 + -132 Combine like terms: 132 + -132 = 0 -129 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -64.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '64.5' to each side of the equation. -64.5 + 1.5x + 64.5 + x2 = 0 + 64.5 Reorder the terms: -64.5 + 64.5 + 1.5x + x2 = 0 + 64.5 Combine like terms: -64.5 + 64.5 = 0.0 0.0 + 1.5x + x2 = 0 + 64.5 1.5x + x2 = 0 + 64.5 Combine like terms: 0 + 64.5 = 64.5 1.5x + x2 = 64.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 64.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 64.5 + 0.5625 Combine like terms: 64.5 + 0.5625 = 65.0625 0.5625 + 1.5x + x2 = 65.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 65.0625 Calculate the square root of the right side: 8.066132902 Break this problem into two subproblems by setting (x + 0.75) equal to 8.066132902 and -8.066132902.Subproblem 1
x + 0.75 = 8.066132902 Simplifying x + 0.75 = 8.066132902 Reorder the terms: 0.75 + x = 8.066132902 Solving 0.75 + x = 8.066132902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 8.066132902 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 8.066132902 + -0.75 x = 8.066132902 + -0.75 Combine like terms: 8.066132902 + -0.75 = 7.316132902 x = 7.316132902 Simplifying x = 7.316132902Subproblem 2
x + 0.75 = -8.066132902 Simplifying x + 0.75 = -8.066132902 Reorder the terms: 0.75 + x = -8.066132902 Solving 0.75 + x = -8.066132902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -8.066132902 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -8.066132902 + -0.75 x = -8.066132902 + -0.75 Combine like terms: -8.066132902 + -0.75 = -8.816132902 x = -8.816132902 Simplifying x = -8.816132902Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.316132902, -8.816132902}
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