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Simplifying x(x + 1) + (x + 2) = 153 Reorder the terms: x(1 + x) + (x + 2) = 153 (1 * x + x * x) + (x + 2) = 153 (1x + x2) + (x + 2) = 153 Reorder the terms: 1x + x2 + (2 + x) = 153 Remove parenthesis around (2 + x) 1x + x2 + 2 + x = 153 Reorder the terms: 2 + 1x + x + x2 = 153 Combine like terms: 1x + x = 2x 2 + 2x + x2 = 153 Solving 2 + 2x + x2 = 153 Solving for variable 'x'. Reorder the terms: 2 + -153 + 2x + x2 = 153 + -153 Combine like terms: 2 + -153 = -151 -151 + 2x + x2 = 153 + -153 Combine like terms: 153 + -153 = 0 -151 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '151' to each side of the equation. -151 + 2x + 151 + x2 = 0 + 151 Reorder the terms: -151 + 151 + 2x + x2 = 0 + 151 Combine like terms: -151 + 151 = 0 0 + 2x + x2 = 0 + 151 2x + x2 = 0 + 151 Combine like terms: 0 + 151 = 151 2x + x2 = 151 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 = 151 + 1 Reorder the terms: 1 + 2x + x2 = 151 + 1 Combine like terms: 151 + 1 = 152 1 + 2x + x2 = 152 Factor a perfect square on the left side: (x + 1)(x + 1) = 152 Calculate the square root of the right side: 12.328828006 Break this problem into two subproblems by setting (x + 1) equal to 12.328828006 and -12.328828006.Subproblem 1
x + 1 = 12.328828006 Simplifying x + 1 = 12.328828006 Reorder the terms: 1 + x = 12.328828006 Solving 1 + x = 12.328828006 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 = 12.328828006 + -1 Combine like terms: 1 + -1 = 0 0 + x = 12.328828006 + -1 x = 12.328828006 + -1 Combine like terms: 12.328828006 + -1 = 11.328828006 x = 11.328828006 Simplifying x = 11.328828006Subproblem 2
x + 1 = -12.328828006 Simplifying x + 1 = -12.328828006 Reorder the terms: 1 + x = -12.328828006 Solving 1 + x = -12.328828006 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 = -12.328828006 + -1 Combine like terms: 1 + -1 = 0 0 + x = -12.328828006 + -1 x = -12.328828006 + -1 Combine like terms: -12.328828006 + -1 = -13.328828006 x = -13.328828006 Simplifying x = -13.328828006Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.328828006, -13.328828006}
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