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Simplifying (20 + -2x)(30 + -2x) = 404 Multiply (20 + -2x) * (30 + -2x) (20(30 + -2x) + -2x * (30 + -2x)) = 404 ((30 * 20 + -2x * 20) + -2x * (30 + -2x)) = 404 ((600 + -40x) + -2x * (30 + -2x)) = 404 (600 + -40x + (30 * -2x + -2x * -2x)) = 404 (600 + -40x + (-60x + 4x2)) = 404 Combine like terms: -40x + -60x = -100x (600 + -100x + 4x2) = 404 Solving 600 + -100x + 4x2 = 404 Solving for variable 'x'. Reorder the terms: 600 + -404 + -100x + 4x2 = 404 + -404 Combine like terms: 600 + -404 = 196 196 + -100x + 4x2 = 404 + -404 Combine like terms: 404 + -404 = 0 196 + -100x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(49 + -25x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(49 + -25x + x2)' equal to zero and attempt to solve: Simplifying 49 + -25x + x2 = 0 Solving 49 + -25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -25x + -49 + x2 = 0 + -49 Reorder the terms: 49 + -49 + -25x + x2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -25x + x2 = 0 + -49 -25x + x2 = 0 + -49 Combine like terms: 0 + -49 = -49 -25x + x2 = -49 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 = -49 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -49 + 156.25 Combine like terms: -49 + 156.25 = 107.25 156.25 + -25x + x2 = 107.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 107.25 Calculate the square root of the right side: 10.356157589 Break this problem into two subproblems by setting (x + -12.5) equal to 10.356157589 and -10.356157589.Subproblem 1
x + -12.5 = 10.356157589 Simplifying x + -12.5 = 10.356157589 Reorder the terms: -12.5 + x = 10.356157589 Solving -12.5 + x = 10.356157589 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 = 10.356157589 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 10.356157589 + 12.5 x = 10.356157589 + 12.5 Combine like terms: 10.356157589 + 12.5 = 22.856157589 x = 22.856157589 Simplifying x = 22.856157589Subproblem 2
x + -12.5 = -10.356157589 Simplifying x + -12.5 = -10.356157589 Reorder the terms: -12.5 + x = -10.356157589 Solving -12.5 + x = -10.356157589 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 = -10.356157589 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -10.356157589 + 12.5 x = -10.356157589 + 12.5 Combine like terms: -10.356157589 + 12.5 = 2.143842411 x = 2.143842411 Simplifying x = 2.143842411Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.856157589, 2.143842411}Solution
x = {22.856157589, 2.143842411}
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