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Simplifying (2x + 5)(x + -1) = 120 Reorder the terms: (5 + 2x)(x + -1) = 120 Reorder the terms: (5 + 2x)(-1 + x) = 120 Multiply (5 + 2x) * (-1 + x) (5(-1 + x) + 2x * (-1 + x)) = 120 ((-1 * 5 + x * 5) + 2x * (-1 + x)) = 120 ((-5 + 5x) + 2x * (-1 + x)) = 120 (-5 + 5x + (-1 * 2x + x * 2x)) = 120 (-5 + 5x + (-2x + 2x2)) = 120 Combine like terms: 5x + -2x = 3x (-5 + 3x + 2x2) = 120 Solving -5 + 3x + 2x2 = 120 Solving for variable 'x'. Reorder the terms: -5 + -120 + 3x + 2x2 = 120 + -120 Combine like terms: -5 + -120 = -125 -125 + 3x + 2x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -125 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -62.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '62.5' to each side of the equation. -62.5 + 1.5x + 62.5 + x2 = 0 + 62.5 Reorder the terms: -62.5 + 62.5 + 1.5x + x2 = 0 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + 1.5x + x2 = 0 + 62.5 1.5x + x2 = 0 + 62.5 Combine like terms: 0 + 62.5 = 62.5 1.5x + x2 = 62.5 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 = 62.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 62.5 + 0.5625 Combine like terms: 62.5 + 0.5625 = 63.0625 0.5625 + 1.5x + x2 = 63.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 63.0625 Calculate the square root of the right side: 7.941190087 Break this problem into two subproblems by setting (x + 0.75) equal to 7.941190087 and -7.941190087.Subproblem 1
x + 0.75 = 7.941190087 Simplifying x + 0.75 = 7.941190087 Reorder the terms: 0.75 + x = 7.941190087 Solving 0.75 + x = 7.941190087 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 = 7.941190087 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 7.941190087 + -0.75 x = 7.941190087 + -0.75 Combine like terms: 7.941190087 + -0.75 = 7.191190087 x = 7.191190087 Simplifying x = 7.191190087Subproblem 2
x + 0.75 = -7.941190087 Simplifying x + 0.75 = -7.941190087 Reorder the terms: 0.75 + x = -7.941190087 Solving 0.75 + x = -7.941190087 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 = -7.941190087 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -7.941190087 + -0.75 x = -7.941190087 + -0.75 Combine like terms: -7.941190087 + -0.75 = -8.691190087 x = -8.691190087 Simplifying x = -8.691190087Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.191190087, -8.691190087}
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