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Simplifying (15 + x)(10 + x) = 240 Multiply (15 + x) * (10 + x) (15(10 + x) + x(10 + x)) = 240 ((10 * 15 + x * 15) + x(10 + x)) = 240 ((150 + 15x) + x(10 + x)) = 240 (150 + 15x + (10 * x + x * x)) = 240 (150 + 15x + (10x + x2)) = 240 Combine like terms: 15x + 10x = 25x (150 + 25x + x2) = 240 Solving 150 + 25x + x2 = 240 Solving for variable 'x'. Reorder the terms: 150 + -240 + 25x + x2 = 240 + -240 Combine like terms: 150 + -240 = -90 -90 + 25x + x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -90 + 25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 25x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 25x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 25x + x2 = 0 + 90 25x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 25x + x2 = 90 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 90 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 90 + 156.25 Combine like terms: 90 + 156.25 = 246.25 156.25 + 25x + x2 = 246.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 246.25 Calculate the square root of the right side: 15.692354826 Break this problem into two subproblems by setting (x + 12.5) equal to 15.692354826 and -15.692354826.Subproblem 1
x + 12.5 = 15.692354826 Simplifying x + 12.5 = 15.692354826 Reorder the terms: 12.5 + x = 15.692354826 Solving 12.5 + x = 15.692354826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 15.692354826 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 15.692354826 + -12.5 x = 15.692354826 + -12.5 Combine like terms: 15.692354826 + -12.5 = 3.192354826 x = 3.192354826 Simplifying x = 3.192354826Subproblem 2
x + 12.5 = -15.692354826 Simplifying x + 12.5 = -15.692354826 Reorder the terms: 12.5 + x = -15.692354826 Solving 12.5 + x = -15.692354826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -15.692354826 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -15.692354826 + -12.5 x = -15.692354826 + -12.5 Combine like terms: -15.692354826 + -12.5 = -28.192354826 x = -28.192354826 Simplifying x = -28.192354826Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.192354826, -28.192354826}
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