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Simplifying (x + 10)(x + -5) = (x + 1) * 2 Reorder the terms: (10 + x)(x + -5) = (x + 1) * 2 Reorder the terms: (10 + x)(-5 + x) = (x + 1) * 2 Multiply (10 + x) * (-5 + x) (10(-5 + x) + x(-5 + x)) = (x + 1) * 2 ((-5 * 10 + x * 10) + x(-5 + x)) = (x + 1) * 2 ((-50 + 10x) + x(-5 + x)) = (x + 1) * 2 (-50 + 10x + (-5 * x + x * x)) = (x + 1) * 2 (-50 + 10x + (-5x + x2)) = (x + 1) * 2 Combine like terms: 10x + -5x = 5x (-50 + 5x + x2) = (x + 1) * 2 Reorder the terms: -50 + 5x + x2 = (1 + x) * 2 Reorder the terms for easier multiplication: -50 + 5x + x2 = 2(1 + x) -50 + 5x + x2 = (1 * 2 + x * 2) -50 + 5x + x2 = (2 + 2x) Solving -50 + 5x + x2 = 2 + 2x Solving for variable 'x'. Reorder the terms: -50 + -2 + 5x + -2x + x2 = 2 + 2x + -2 + -2x Combine like terms: -50 + -2 = -52 -52 + 5x + -2x + x2 = 2 + 2x + -2 + -2x Combine like terms: 5x + -2x = 3x -52 + 3x + x2 = 2 + 2x + -2 + -2x Reorder the terms: -52 + 3x + x2 = 2 + -2 + 2x + -2x Combine like terms: 2 + -2 = 0 -52 + 3x + x2 = 0 + 2x + -2x -52 + 3x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -52 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + 3x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + 3x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 3x + x2 = 0 + 52 3x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 3x + x2 = 52 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 = 52 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 52 + 2.25 Combine like terms: 52 + 2.25 = 54.25 2.25 + 3x + x2 = 54.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (x + 1.5) equal to 7.365459931 and -7.365459931.Subproblem 1
x + 1.5 = 7.365459931 Simplifying x + 1.5 = 7.365459931 Reorder the terms: 1.5 + x = 7.365459931 Solving 1.5 + x = 7.365459931 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 = 7.365459931 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.365459931 + -1.5 x = 7.365459931 + -1.5 Combine like terms: 7.365459931 + -1.5 = 5.865459931 x = 5.865459931 Simplifying x = 5.865459931Subproblem 2
x + 1.5 = -7.365459931 Simplifying x + 1.5 = -7.365459931 Reorder the terms: 1.5 + x = -7.365459931 Solving 1.5 + x = -7.365459931 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 = -7.365459931 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.365459931 + -1.5 x = -7.365459931 + -1.5 Combine like terms: -7.365459931 + -1.5 = -8.865459931 x = -8.865459931 Simplifying x = -8.865459931Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.865459931, -8.865459931}
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