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Simplifying (2x + 20)(2x + 30) = 5000 Reorder the terms: (20 + 2x)(2x + 30) = 5000 Reorder the terms: (20 + 2x)(30 + 2x) = 5000 Multiply (20 + 2x) * (30 + 2x) (20(30 + 2x) + 2x * (30 + 2x)) = 5000 ((30 * 20 + 2x * 20) + 2x * (30 + 2x)) = 5000 ((600 + 40x) + 2x * (30 + 2x)) = 5000 (600 + 40x + (30 * 2x + 2x * 2x)) = 5000 (600 + 40x + (60x + 4x2)) = 5000 Combine like terms: 40x + 60x = 100x (600 + 100x + 4x2) = 5000 Solving 600 + 100x + 4x2 = 5000 Solving for variable 'x'. Reorder the terms: 600 + -5000 + 100x + 4x2 = 5000 + -5000 Combine like terms: 600 + -5000 = -4400 -4400 + 100x + 4x2 = 5000 + -5000 Combine like terms: 5000 + -5000 = 0 -4400 + 100x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1100 + 25x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1100 + 25x + x2)' equal to zero and attempt to solve: Simplifying -1100 + 25x + x2 = 0 Solving -1100 + 25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1100' to each side of the equation. -1100 + 25x + 1100 + x2 = 0 + 1100 Reorder the terms: -1100 + 1100 + 25x + x2 = 0 + 1100 Combine like terms: -1100 + 1100 = 0 0 + 25x + x2 = 0 + 1100 25x + x2 = 0 + 1100 Combine like terms: 0 + 1100 = 1100 25x + x2 = 1100 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 = 1100 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 1100 + 156.25 Combine like terms: 1100 + 156.25 = 1256.25 156.25 + 25x + x2 = 1256.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 1256.25 Calculate the square root of the right side: 35.443617197 Break this problem into two subproblems by setting (x + 12.5) equal to 35.443617197 and -35.443617197.Subproblem 1
x + 12.5 = 35.443617197 Simplifying x + 12.5 = 35.443617197 Reorder the terms: 12.5 + x = 35.443617197 Solving 12.5 + x = 35.443617197 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 = 35.443617197 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 35.443617197 + -12.5 x = 35.443617197 + -12.5 Combine like terms: 35.443617197 + -12.5 = 22.943617197 x = 22.943617197 Simplifying x = 22.943617197Subproblem 2
x + 12.5 = -35.443617197 Simplifying x + 12.5 = -35.443617197 Reorder the terms: 12.5 + x = -35.443617197 Solving 12.5 + x = -35.443617197 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 = -35.443617197 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -35.443617197 + -12.5 x = -35.443617197 + -12.5 Combine like terms: -35.443617197 + -12.5 = -47.943617197 x = -47.943617197 Simplifying x = -47.943617197Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.943617197, -47.943617197}Solution
x = {22.943617197, -47.943617197}
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