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Simplifying (2x + 50)(2x + 20) = 2000 Reorder the terms: (50 + 2x)(2x + 20) = 2000 Reorder the terms: (50 + 2x)(20 + 2x) = 2000 Multiply (50 + 2x) * (20 + 2x) (50(20 + 2x) + 2x * (20 + 2x)) = 2000 ((20 * 50 + 2x * 50) + 2x * (20 + 2x)) = 2000 ((1000 + 100x) + 2x * (20 + 2x)) = 2000 (1000 + 100x + (20 * 2x + 2x * 2x)) = 2000 (1000 + 100x + (40x + 4x2)) = 2000 Combine like terms: 100x + 40x = 140x (1000 + 140x + 4x2) = 2000 Solving 1000 + 140x + 4x2 = 2000 Solving for variable 'x'. Reorder the terms: 1000 + -2000 + 140x + 4x2 = 2000 + -2000 Combine like terms: 1000 + -2000 = -1000 -1000 + 140x + 4x2 = 2000 + -2000 Combine like terms: 2000 + -2000 = 0 -1000 + 140x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-250 + 35x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-250 + 35x + x2)' equal to zero and attempt to solve: Simplifying -250 + 35x + x2 = 0 Solving -250 + 35x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + 35x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + 35x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 35x + x2 = 0 + 250 35x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 35x + x2 = 250 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = 250 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 250 + 306.25 Combine like terms: 250 + 306.25 = 556.25 306.25 + 35x + x2 = 556.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 556.25 Calculate the square root of the right side: 23.58495283 Break this problem into two subproblems by setting (x + 17.5) equal to 23.58495283 and -23.58495283.Subproblem 1
x + 17.5 = 23.58495283 Simplifying x + 17.5 = 23.58495283 Reorder the terms: 17.5 + x = 23.58495283 Solving 17.5 + x = 23.58495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 23.58495283 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 23.58495283 + -17.5 x = 23.58495283 + -17.5 Combine like terms: 23.58495283 + -17.5 = 6.08495283 x = 6.08495283 Simplifying x = 6.08495283Subproblem 2
x + 17.5 = -23.58495283 Simplifying x + 17.5 = -23.58495283 Reorder the terms: 17.5 + x = -23.58495283 Solving 17.5 + x = -23.58495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -23.58495283 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -23.58495283 + -17.5 x = -23.58495283 + -17.5 Combine like terms: -23.58495283 + -17.5 = -41.08495283 x = -41.08495283 Simplifying x = -41.08495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.08495283, -41.08495283}Solution
x = {6.08495283, -41.08495283}
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