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Simplifying (x + 10)(x + 5) = 180 Reorder the terms: (10 + x)(x + 5) = 180 Reorder the terms: (10 + x)(5 + x) = 180 Multiply (10 + x) * (5 + x) (10(5 + x) + x(5 + x)) = 180 ((5 * 10 + x * 10) + x(5 + x)) = 180 ((50 + 10x) + x(5 + x)) = 180 (50 + 10x + (5 * x + x * x)) = 180 (50 + 10x + (5x + x2)) = 180 Combine like terms: 10x + 5x = 15x (50 + 15x + x2) = 180 Solving 50 + 15x + x2 = 180 Solving for variable 'x'. Reorder the terms: 50 + -180 + 15x + x2 = 180 + -180 Combine like terms: 50 + -180 = -130 -130 + 15x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -130 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + 15x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + 15x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 15x + x2 = 0 + 130 15x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 15x + x2 = 130 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 130 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 130 + 56.25 Combine like terms: 130 + 56.25 = 186.25 56.25 + 15x + x2 = 186.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 186.25 Calculate the square root of the right side: 13.647344064 Break this problem into two subproblems by setting (x + 7.5) equal to 13.647344064 and -13.647344064.Subproblem 1
x + 7.5 = 13.647344064 Simplifying x + 7.5 = 13.647344064 Reorder the terms: 7.5 + x = 13.647344064 Solving 7.5 + x = 13.647344064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 13.647344064 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 13.647344064 + -7.5 x = 13.647344064 + -7.5 Combine like terms: 13.647344064 + -7.5 = 6.147344064 x = 6.147344064 Simplifying x = 6.147344064Subproblem 2
x + 7.5 = -13.647344064 Simplifying x + 7.5 = -13.647344064 Reorder the terms: 7.5 + x = -13.647344064 Solving 7.5 + x = -13.647344064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -13.647344064 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -13.647344064 + -7.5 x = -13.647344064 + -7.5 Combine like terms: -13.647344064 + -7.5 = -21.147344064 x = -21.147344064 Simplifying x = -21.147344064Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.147344064, -21.147344064}
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