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Simplifying 2x2 + -86x + 208 = 0 Reorder the terms: 208 + -86x + 2x2 = 0 Solving 208 + -86x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(104 + -43x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(104 + -43x + x2)' equal to zero and attempt to solve: Simplifying 104 + -43x + x2 = 0 Solving 104 + -43x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-104' to each side of the equation. 104 + -43x + -104 + x2 = 0 + -104 Reorder the terms: 104 + -104 + -43x + x2 = 0 + -104 Combine like terms: 104 + -104 = 0 0 + -43x + x2 = 0 + -104 -43x + x2 = 0 + -104 Combine like terms: 0 + -104 = -104 -43x + x2 = -104 The x term is -43x. Take half its coefficient (-21.5). Square it (462.25) and add it to both sides. Add '462.25' to each side of the equation. -43x + 462.25 + x2 = -104 + 462.25 Reorder the terms: 462.25 + -43x + x2 = -104 + 462.25 Combine like terms: -104 + 462.25 = 358.25 462.25 + -43x + x2 = 358.25 Factor a perfect square on the left side: (x + -21.5)(x + -21.5) = 358.25 Calculate the square root of the right side: 18.927493231 Break this problem into two subproblems by setting (x + -21.5) equal to 18.927493231 and -18.927493231.Subproblem 1
x + -21.5 = 18.927493231 Simplifying x + -21.5 = 18.927493231 Reorder the terms: -21.5 + x = 18.927493231 Solving -21.5 + x = 18.927493231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.5' to each side of the equation. -21.5 + 21.5 + x = 18.927493231 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + x = 18.927493231 + 21.5 x = 18.927493231 + 21.5 Combine like terms: 18.927493231 + 21.5 = 40.427493231 x = 40.427493231 Simplifying x = 40.427493231Subproblem 2
x + -21.5 = -18.927493231 Simplifying x + -21.5 = -18.927493231 Reorder the terms: -21.5 + x = -18.927493231 Solving -21.5 + x = -18.927493231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.5' to each side of the equation. -21.5 + 21.5 + x = -18.927493231 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + x = -18.927493231 + 21.5 x = -18.927493231 + 21.5 Combine like terms: -18.927493231 + 21.5 = 2.572506769 x = 2.572506769 Simplifying x = 2.572506769Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.427493231, 2.572506769}Solution
x = {40.427493231, 2.572506769}
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