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Simplifying x2 + -400x + 8600 = 0 Reorder the terms: 8600 + -400x + x2 = 0 Solving 8600 + -400x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8600' to each side of the equation. 8600 + -400x + -8600 + x2 = 0 + -8600 Reorder the terms: 8600 + -8600 + -400x + x2 = 0 + -8600 Combine like terms: 8600 + -8600 = 0 0 + -400x + x2 = 0 + -8600 -400x + x2 = 0 + -8600 Combine like terms: 0 + -8600 = -8600 -400x + x2 = -8600 The x term is -400x. Take half its coefficient (-200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. -400x + 40000 + x2 = -8600 + 40000 Reorder the terms: 40000 + -400x + x2 = -8600 + 40000 Combine like terms: -8600 + 40000 = 31400 40000 + -400x + x2 = 31400 Factor a perfect square on the left side: (x + -200)(x + -200) = 31400 Calculate the square root of the right side: 177.200451467 Break this problem into two subproblems by setting (x + -200) equal to 177.200451467 and -177.200451467.Subproblem 1
x + -200 = 177.200451467 Simplifying x + -200 = 177.200451467 Reorder the terms: -200 + x = 177.200451467 Solving -200 + x = 177.200451467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = 177.200451467 + 200 Combine like terms: -200 + 200 = 0 0 + x = 177.200451467 + 200 x = 177.200451467 + 200 Combine like terms: 177.200451467 + 200 = 377.200451467 x = 377.200451467 Simplifying x = 377.200451467Subproblem 2
x + -200 = -177.200451467 Simplifying x + -200 = -177.200451467 Reorder the terms: -200 + x = -177.200451467 Solving -200 + x = -177.200451467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = -177.200451467 + 200 Combine like terms: -200 + 200 = 0 0 + x = -177.200451467 + 200 x = -177.200451467 + 200 Combine like terms: -177.200451467 + 200 = 22.799548533 x = 22.799548533 Simplifying x = 22.799548533Solution
The solution to the problem is based on the solutions from the subproblems. x = {377.200451467, 22.799548533}
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