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Simplifying x2 + -200x + 8555.5 = 0 Reorder the terms: 8555.5 + -200x + x2 = 0 Solving 8555.5 + -200x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8555.5' to each side of the equation. 8555.5 + -200x + -8555.5 + x2 = 0 + -8555.5 Reorder the terms: 8555.5 + -8555.5 + -200x + x2 = 0 + -8555.5 Combine like terms: 8555.5 + -8555.5 = 0.0 0.0 + -200x + x2 = 0 + -8555.5 -200x + x2 = 0 + -8555.5 Combine like terms: 0 + -8555.5 = -8555.5 -200x + x2 = -8555.5 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -8555.5 + 10000 Reorder the terms: 10000 + -200x + x2 = -8555.5 + 10000 Combine like terms: -8555.5 + 10000 = 1444.5 10000 + -200x + x2 = 1444.5 Factor a perfect square on the left side: (x + -100)(x + -100) = 1444.5 Calculate the square root of the right side: 38.006578378 Break this problem into two subproblems by setting (x + -100) equal to 38.006578378 and -38.006578378.Subproblem 1
x + -100 = 38.006578378 Simplifying x + -100 = 38.006578378 Reorder the terms: -100 + x = 38.006578378 Solving -100 + x = 38.006578378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 38.006578378 + 100 Combine like terms: -100 + 100 = 0 0 + x = 38.006578378 + 100 x = 38.006578378 + 100 Combine like terms: 38.006578378 + 100 = 138.006578378 x = 138.006578378 Simplifying x = 138.006578378Subproblem 2
x + -100 = -38.006578378 Simplifying x + -100 = -38.006578378 Reorder the terms: -100 + x = -38.006578378 Solving -100 + x = -38.006578378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -38.006578378 + 100 Combine like terms: -100 + 100 = 0 0 + x = -38.006578378 + 100 x = -38.006578378 + 100 Combine like terms: -38.006578378 + 100 = 61.993421622 x = 61.993421622 Simplifying x = 61.993421622Solution
The solution to the problem is based on the solutions from the subproblems. x = {138.006578378, 61.993421622}
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