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Simplifying (x + 1)(x + 2) = 120 Reorder the terms: (1 + x)(x + 2) = 120 Reorder the terms: (1 + x)(2 + x) = 120 Multiply (1 + x) * (2 + x) (1(2 + x) + x(2 + x)) = 120 ((2 * 1 + x * 1) + x(2 + x)) = 120 ((2 + 1x) + x(2 + x)) = 120 (2 + 1x + (2 * x + x * x)) = 120 (2 + 1x + (2x + x2)) = 120 Combine like terms: 1x + 2x = 3x (2 + 3x + x2) = 120 Solving 2 + 3x + x2 = 120 Solving for variable 'x'. Reorder the terms: 2 + -120 + 3x + x2 = 120 + -120 Combine like terms: 2 + -120 = -118 -118 + 3x + x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -118 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '118' to each side of the equation. -118 + 3x + 118 + x2 = 0 + 118 Reorder the terms: -118 + 118 + 3x + x2 = 0 + 118 Combine like terms: -118 + 118 = 0 0 + 3x + x2 = 0 + 118 3x + x2 = 0 + 118 Combine like terms: 0 + 118 = 118 3x + x2 = 118 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 = 118 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 118 + 2.25 Combine like terms: 118 + 2.25 = 120.25 2.25 + 3x + x2 = 120.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + 1.5) equal to 10.9658561 and -10.9658561.Subproblem 1
x + 1.5 = 10.9658561 Simplifying x + 1.5 = 10.9658561 Reorder the terms: 1.5 + x = 10.9658561 Solving 1.5 + x = 10.9658561 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 = 10.9658561 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 10.9658561 + -1.5 x = 10.9658561 + -1.5 Combine like terms: 10.9658561 + -1.5 = 9.4658561 x = 9.4658561 Simplifying x = 9.4658561Subproblem 2
x + 1.5 = -10.9658561 Simplifying x + 1.5 = -10.9658561 Reorder the terms: 1.5 + x = -10.9658561 Solving 1.5 + x = -10.9658561 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 = -10.9658561 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -10.9658561 + -1.5 x = -10.9658561 + -1.5 Combine like terms: -10.9658561 + -1.5 = -12.4658561 x = -12.4658561 Simplifying x = -12.4658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.4658561, -12.4658561}
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