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Simplifying (60 + -2x)(40 + -2x) = 2000 Multiply (60 + -2x) * (40 + -2x) (60(40 + -2x) + -2x * (40 + -2x)) = 2000 ((40 * 60 + -2x * 60) + -2x * (40 + -2x)) = 2000 ((2400 + -120x) + -2x * (40 + -2x)) = 2000 (2400 + -120x + (40 * -2x + -2x * -2x)) = 2000 (2400 + -120x + (-80x + 4x2)) = 2000 Combine like terms: -120x + -80x = -200x (2400 + -200x + 4x2) = 2000 Solving 2400 + -200x + 4x2 = 2000 Solving for variable 'x'. Reorder the terms: 2400 + -2000 + -200x + 4x2 = 2000 + -2000 Combine like terms: 2400 + -2000 = 400 400 + -200x + 4x2 = 2000 + -2000 Combine like terms: 2000 + -2000 = 0 400 + -200x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(100 + -50x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(100 + -50x + x2)' equal to zero and attempt to solve: Simplifying 100 + -50x + x2 = 0 Solving 100 + -50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -50x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -50x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -50x + x2 = 0 + -100 -50x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -50x + x2 = -100 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 = -100 + 625 Reorder the terms: 625 + -50x + x2 = -100 + 625 Combine like terms: -100 + 625 = 525 625 + -50x + x2 = 525 Factor a perfect square on the left side: (x + -25)(x + -25) = 525 Calculate the square root of the right side: 22.912878475 Break this problem into two subproblems by setting (x + -25) equal to 22.912878475 and -22.912878475.Subproblem 1
x + -25 = 22.912878475 Simplifying x + -25 = 22.912878475 Reorder the terms: -25 + x = 22.912878475 Solving -25 + x = 22.912878475 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 = 22.912878475 + 25 Combine like terms: -25 + 25 = 0 0 + x = 22.912878475 + 25 x = 22.912878475 + 25 Combine like terms: 22.912878475 + 25 = 47.912878475 x = 47.912878475 Simplifying x = 47.912878475Subproblem 2
x + -25 = -22.912878475 Simplifying x + -25 = -22.912878475 Reorder the terms: -25 + x = -22.912878475 Solving -25 + x = -22.912878475 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 = -22.912878475 + 25 Combine like terms: -25 + 25 = 0 0 + x = -22.912878475 + 25 x = -22.912878475 + 25 Combine like terms: -22.912878475 + 25 = 2.087121525 x = 2.087121525 Simplifying x = 2.087121525Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.912878475, 2.087121525}Solution
x = {47.912878475, 2.087121525}
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