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Simplifying (60 + -2x)(40 + -2x) = 6000 Multiply (60 + -2x) * (40 + -2x) (60(40 + -2x) + -2x * (40 + -2x)) = 6000 ((40 * 60 + -2x * 60) + -2x * (40 + -2x)) = 6000 ((2400 + -120x) + -2x * (40 + -2x)) = 6000 (2400 + -120x + (40 * -2x + -2x * -2x)) = 6000 (2400 + -120x + (-80x + 4x2)) = 6000 Combine like terms: -120x + -80x = -200x (2400 + -200x + 4x2) = 6000 Solving 2400 + -200x + 4x2 = 6000 Solving for variable 'x'. Reorder the terms: 2400 + -6000 + -200x + 4x2 = 6000 + -6000 Combine like terms: 2400 + -6000 = -3600 -3600 + -200x + 4x2 = 6000 + -6000 Combine like terms: 6000 + -6000 = 0 -3600 + -200x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-900 + -50x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-900 + -50x + x2)' equal to zero and attempt to solve: Simplifying -900 + -50x + x2 = 0 Solving -900 + -50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '900' to each side of the equation. -900 + -50x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + -50x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + -50x + x2 = 0 + 900 -50x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 -50x + x2 = 900 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 = 900 + 625 Reorder the terms: 625 + -50x + x2 = 900 + 625 Combine like terms: 900 + 625 = 1525 625 + -50x + x2 = 1525 Factor a perfect square on the left side: (x + -25)(x + -25) = 1525 Calculate the square root of the right side: 39.05124838 Break this problem into two subproblems by setting (x + -25) equal to 39.05124838 and -39.05124838.Subproblem 1
x + -25 = 39.05124838 Simplifying x + -25 = 39.05124838 Reorder the terms: -25 + x = 39.05124838 Solving -25 + x = 39.05124838 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 = 39.05124838 + 25 Combine like terms: -25 + 25 = 0 0 + x = 39.05124838 + 25 x = 39.05124838 + 25 Combine like terms: 39.05124838 + 25 = 64.05124838 x = 64.05124838 Simplifying x = 64.05124838Subproblem 2
x + -25 = -39.05124838 Simplifying x + -25 = -39.05124838 Reorder the terms: -25 + x = -39.05124838 Solving -25 + x = -39.05124838 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 = -39.05124838 + 25 Combine like terms: -25 + 25 = 0 0 + x = -39.05124838 + 25 x = -39.05124838 + 25 Combine like terms: -39.05124838 + 25 = -14.05124838 x = -14.05124838 Simplifying x = -14.05124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {64.05124838, -14.05124838}Solution
x = {64.05124838, -14.05124838}
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