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Simplifying x(x + 3) = 151 Reorder the terms: x(3 + x) = 151 (3 * x + x * x) = 151 (3x + x2) = 151 Solving 3x + x2 = 151 Solving for variable 'x'. Reorder the terms: -151 + 3x + x2 = 151 + -151 Combine like terms: 151 + -151 = 0 -151 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '151' to each side of the equation. -151 + 3x + 151 + x2 = 0 + 151 Reorder the terms: -151 + 151 + 3x + x2 = 0 + 151 Combine like terms: -151 + 151 = 0 0 + 3x + x2 = 0 + 151 3x + x2 = 0 + 151 Combine like terms: 0 + 151 = 151 3x + x2 = 151 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 151 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 151 + 2.25 Combine like terms: 151 + 2.25 = 153.25 2.25 + 3x + x2 = 153.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 153.25 Calculate the square root of the right side: 12.379418403 Break this problem into two subproblems by setting (x + 1.5) equal to 12.379418403 and -12.379418403.Subproblem 1
x + 1.5 = 12.379418403 Simplifying x + 1.5 = 12.379418403 Reorder the terms: 1.5 + x = 12.379418403 Solving 1.5 + x = 12.379418403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 12.379418403 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.379418403 + -1.5 x = 12.379418403 + -1.5 Combine like terms: 12.379418403 + -1.5 = 10.879418403 x = 10.879418403 Simplifying x = 10.879418403Subproblem 2
x + 1.5 = -12.379418403 Simplifying x + 1.5 = -12.379418403 Reorder the terms: 1.5 + x = -12.379418403 Solving 1.5 + x = -12.379418403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -12.379418403 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.379418403 + -1.5 x = -12.379418403 + -1.5 Combine like terms: -12.379418403 + -1.5 = -13.879418403 x = -13.879418403 Simplifying x = -13.879418403Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.879418403, -13.879418403}
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