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Simplifying (40 + 2x)(60 + 2x) = 5000 Multiply (40 + 2x) * (60 + 2x) (40(60 + 2x) + 2x * (60 + 2x)) = 5000 ((60 * 40 + 2x * 40) + 2x * (60 + 2x)) = 5000 ((2400 + 80x) + 2x * (60 + 2x)) = 5000 (2400 + 80x + (60 * 2x + 2x * 2x)) = 5000 (2400 + 80x + (120x + 4x2)) = 5000 Combine like terms: 80x + 120x = 200x (2400 + 200x + 4x2) = 5000 Solving 2400 + 200x + 4x2 = 5000 Solving for variable 'x'. Reorder the terms: 2400 + -5000 + 200x + 4x2 = 5000 + -5000 Combine like terms: 2400 + -5000 = -2600 -2600 + 200x + 4x2 = 5000 + -5000 Combine like terms: 5000 + -5000 = 0 -2600 + 200x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-650 + 50x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-650 + 50x + x2)' equal to zero and attempt to solve: Simplifying -650 + 50x + x2 = 0 Solving -650 + 50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '650' to each side of the equation. -650 + 50x + 650 + x2 = 0 + 650 Reorder the terms: -650 + 650 + 50x + x2 = 0 + 650 Combine like terms: -650 + 650 = 0 0 + 50x + x2 = 0 + 650 50x + x2 = 0 + 650 Combine like terms: 0 + 650 = 650 50x + x2 = 650 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 650 + 625 Reorder the terms: 625 + 50x + x2 = 650 + 625 Combine like terms: 650 + 625 = 1275 625 + 50x + x2 = 1275 Factor a perfect square on the left side: (x + 25)(x + 25) = 1275 Calculate the square root of the right side: 35.707142143 Break this problem into two subproblems by setting (x + 25) equal to 35.707142143 and -35.707142143.Subproblem 1
x + 25 = 35.707142143 Simplifying x + 25 = 35.707142143 Reorder the terms: 25 + x = 35.707142143 Solving 25 + x = 35.707142143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 35.707142143 + -25 Combine like terms: 25 + -25 = 0 0 + x = 35.707142143 + -25 x = 35.707142143 + -25 Combine like terms: 35.707142143 + -25 = 10.707142143 x = 10.707142143 Simplifying x = 10.707142143Subproblem 2
x + 25 = -35.707142143 Simplifying x + 25 = -35.707142143 Reorder the terms: 25 + x = -35.707142143 Solving 25 + x = -35.707142143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -35.707142143 + -25 Combine like terms: 25 + -25 = 0 0 + x = -35.707142143 + -25 x = -35.707142143 + -25 Combine like terms: -35.707142143 + -25 = -60.707142143 x = -60.707142143 Simplifying x = -60.707142143Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.707142143, -60.707142143}Solution
x = {10.707142143, -60.707142143}
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