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Simplifying 2x2 + -440x + 16000 = 0 Reorder the terms: 16000 + -440x + 2x2 = 0 Solving 16000 + -440x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(8000 + -220x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8000 + -220x + x2)' equal to zero and attempt to solve: Simplifying 8000 + -220x + x2 = 0 Solving 8000 + -220x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8000' to each side of the equation. 8000 + -220x + -8000 + x2 = 0 + -8000 Reorder the terms: 8000 + -8000 + -220x + x2 = 0 + -8000 Combine like terms: 8000 + -8000 = 0 0 + -220x + x2 = 0 + -8000 -220x + x2 = 0 + -8000 Combine like terms: 0 + -8000 = -8000 -220x + x2 = -8000 The x term is -220x. Take half its coefficient (-110). Square it (12100) and add it to both sides. Add '12100' to each side of the equation. -220x + 12100 + x2 = -8000 + 12100 Reorder the terms: 12100 + -220x + x2 = -8000 + 12100 Combine like terms: -8000 + 12100 = 4100 12100 + -220x + x2 = 4100 Factor a perfect square on the left side: (x + -110)(x + -110) = 4100 Calculate the square root of the right side: 64.031242374 Break this problem into two subproblems by setting (x + -110) equal to 64.031242374 and -64.031242374.Subproblem 1
x + -110 = 64.031242374 Simplifying x + -110 = 64.031242374 Reorder the terms: -110 + x = 64.031242374 Solving -110 + x = 64.031242374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = 64.031242374 + 110 Combine like terms: -110 + 110 = 0 0 + x = 64.031242374 + 110 x = 64.031242374 + 110 Combine like terms: 64.031242374 + 110 = 174.031242374 x = 174.031242374 Simplifying x = 174.031242374Subproblem 2
x + -110 = -64.031242374 Simplifying x + -110 = -64.031242374 Reorder the terms: -110 + x = -64.031242374 Solving -110 + x = -64.031242374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = -64.031242374 + 110 Combine like terms: -110 + 110 = 0 0 + x = -64.031242374 + 110 x = -64.031242374 + 110 Combine like terms: -64.031242374 + 110 = 45.968757626 x = 45.968757626 Simplifying x = 45.968757626Solution
The solution to the problem is based on the solutions from the subproblems. x = {174.031242374, 45.968757626}Solution
x = {174.031242374, 45.968757626}
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