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Simplifying (32 + -2x)(30 + -2x) = 720 Multiply (32 + -2x) * (30 + -2x) (32(30 + -2x) + -2x * (30 + -2x)) = 720 ((30 * 32 + -2x * 32) + -2x * (30 + -2x)) = 720 ((960 + -64x) + -2x * (30 + -2x)) = 720 (960 + -64x + (30 * -2x + -2x * -2x)) = 720 (960 + -64x + (-60x + 4x2)) = 720 Combine like terms: -64x + -60x = -124x (960 + -124x + 4x2) = 720 Solving 960 + -124x + 4x2 = 720 Solving for variable 'x'. Reorder the terms: 960 + -720 + -124x + 4x2 = 720 + -720 Combine like terms: 960 + -720 = 240 240 + -124x + 4x2 = 720 + -720 Combine like terms: 720 + -720 = 0 240 + -124x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(60 + -31x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(60 + -31x + x2)' equal to zero and attempt to solve: Simplifying 60 + -31x + x2 = 0 Solving 60 + -31x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -31x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -31x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -31x + x2 = 0 + -60 -31x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -31x + x2 = -60 The x term is -31x. Take half its coefficient (-15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. -31x + 240.25 + x2 = -60 + 240.25 Reorder the terms: 240.25 + -31x + x2 = -60 + 240.25 Combine like terms: -60 + 240.25 = 180.25 240.25 + -31x + x2 = 180.25 Factor a perfect square on the left side: (x + -15.5)(x + -15.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + -15.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + -15.5 = 13.425721582 Simplifying x + -15.5 = 13.425721582 Reorder the terms: -15.5 + x = 13.425721582 Solving -15.5 + x = 13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = 13.425721582 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = 13.425721582 + 15.5 x = 13.425721582 + 15.5 Combine like terms: 13.425721582 + 15.5 = 28.925721582 x = 28.925721582 Simplifying x = 28.925721582Subproblem 2
x + -15.5 = -13.425721582 Simplifying x + -15.5 = -13.425721582 Reorder the terms: -15.5 + x = -13.425721582 Solving -15.5 + x = -13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = -13.425721582 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = -13.425721582 + 15.5 x = -13.425721582 + 15.5 Combine like terms: -13.425721582 + 15.5 = 2.074278418 x = 2.074278418 Simplifying x = 2.074278418Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.925721582, 2.074278418}Solution
x = {28.925721582, 2.074278418}
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