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Simplifying x2 + -200x + 1125 = 0 Reorder the terms: 1125 + -200x + x2 = 0 Solving 1125 + -200x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1125' to each side of the equation. 1125 + -200x + -1125 + x2 = 0 + -1125 Reorder the terms: 1125 + -1125 + -200x + x2 = 0 + -1125 Combine like terms: 1125 + -1125 = 0 0 + -200x + x2 = 0 + -1125 -200x + x2 = 0 + -1125 Combine like terms: 0 + -1125 = -1125 -200x + x2 = -1125 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 = -1125 + 10000 Reorder the terms: 10000 + -200x + x2 = -1125 + 10000 Combine like terms: -1125 + 10000 = 8875 10000 + -200x + x2 = 8875 Factor a perfect square on the left side: (x + -100)(x + -100) = 8875 Calculate the square root of the right side: 94.207218407 Break this problem into two subproblems by setting (x + -100) equal to 94.207218407 and -94.207218407.Subproblem 1
x + -100 = 94.207218407 Simplifying x + -100 = 94.207218407 Reorder the terms: -100 + x = 94.207218407 Solving -100 + x = 94.207218407 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 = 94.207218407 + 100 Combine like terms: -100 + 100 = 0 0 + x = 94.207218407 + 100 x = 94.207218407 + 100 Combine like terms: 94.207218407 + 100 = 194.207218407 x = 194.207218407 Simplifying x = 194.207218407Subproblem 2
x + -100 = -94.207218407 Simplifying x + -100 = -94.207218407 Reorder the terms: -100 + x = -94.207218407 Solving -100 + x = -94.207218407 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 = -94.207218407 + 100 Combine like terms: -100 + 100 = 0 0 + x = -94.207218407 + 100 x = -94.207218407 + 100 Combine like terms: -94.207218407 + 100 = 5.792781593 x = 5.792781593 Simplifying x = 5.792781593Solution
The solution to the problem is based on the solutions from the subproblems. x = {194.207218407, 5.792781593}
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