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Simplifying 2x2 + -360x + 15500 = 0 Reorder the terms: 15500 + -360x + 2x2 = 0 Solving 15500 + -360x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7750 + -180x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7750 + -180x + x2)' equal to zero and attempt to solve: Simplifying 7750 + -180x + x2 = 0 Solving 7750 + -180x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7750' to each side of the equation. 7750 + -180x + -7750 + x2 = 0 + -7750 Reorder the terms: 7750 + -7750 + -180x + x2 = 0 + -7750 Combine like terms: 7750 + -7750 = 0 0 + -180x + x2 = 0 + -7750 -180x + x2 = 0 + -7750 Combine like terms: 0 + -7750 = -7750 -180x + x2 = -7750 The x term is -180x. Take half its coefficient (-90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. -180x + 8100 + x2 = -7750 + 8100 Reorder the terms: 8100 + -180x + x2 = -7750 + 8100 Combine like terms: -7750 + 8100 = 350 8100 + -180x + x2 = 350 Factor a perfect square on the left side: (x + -90)(x + -90) = 350 Calculate the square root of the right side: 18.708286934 Break this problem into two subproblems by setting (x + -90) equal to 18.708286934 and -18.708286934.Subproblem 1
x + -90 = 18.708286934 Simplifying x + -90 = 18.708286934 Reorder the terms: -90 + x = 18.708286934 Solving -90 + x = 18.708286934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 18.708286934 + 90 Combine like terms: -90 + 90 = 0 0 + x = 18.708286934 + 90 x = 18.708286934 + 90 Combine like terms: 18.708286934 + 90 = 108.708286934 x = 108.708286934 Simplifying x = 108.708286934Subproblem 2
x + -90 = -18.708286934 Simplifying x + -90 = -18.708286934 Reorder the terms: -90 + x = -18.708286934 Solving -90 + x = -18.708286934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = -18.708286934 + 90 Combine like terms: -90 + 90 = 0 0 + x = -18.708286934 + 90 x = -18.708286934 + 90 Combine like terms: -18.708286934 + 90 = 71.291713066 x = 71.291713066 Simplifying x = 71.291713066Solution
The solution to the problem is based on the solutions from the subproblems. x = {108.708286934, 71.291713066}Solution
x = {108.708286934, 71.291713066}
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