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Simplifying x2 + -36x + 200 = 5 Reorder the terms: 200 + -36x + x2 = 5 Solving 200 + -36x + x2 = 5 Solving for variable 'x'. Reorder the terms: 200 + -5 + -36x + x2 = 5 + -5 Combine like terms: 200 + -5 = 195 195 + -36x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 195 + -36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-195' to each side of the equation. 195 + -36x + -195 + x2 = 0 + -195 Reorder the terms: 195 + -195 + -36x + x2 = 0 + -195 Combine like terms: 195 + -195 = 0 0 + -36x + x2 = 0 + -195 -36x + x2 = 0 + -195 Combine like terms: 0 + -195 = -195 -36x + x2 = -195 The x term is -36x. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x + 324 + x2 = -195 + 324 Reorder the terms: 324 + -36x + x2 = -195 + 324 Combine like terms: -195 + 324 = 129 324 + -36x + x2 = 129 Factor a perfect square on the left side: (x + -18)(x + -18) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (x + -18) equal to 11.357816692 and -11.357816692.Subproblem 1
x + -18 = 11.357816692 Simplifying x + -18 = 11.357816692 Reorder the terms: -18 + x = 11.357816692 Solving -18 + x = 11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 11.357816692 + 18 Combine like terms: -18 + 18 = 0 0 + x = 11.357816692 + 18 x = 11.357816692 + 18 Combine like terms: 11.357816692 + 18 = 29.357816692 x = 29.357816692 Simplifying x = 29.357816692Subproblem 2
x + -18 = -11.357816692 Simplifying x + -18 = -11.357816692 Reorder the terms: -18 + x = -11.357816692 Solving -18 + x = -11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -11.357816692 + 18 Combine like terms: -18 + 18 = 0 0 + x = -11.357816692 + 18 x = -11.357816692 + 18 Combine like terms: -11.357816692 + 18 = 6.642183308 x = 6.642183308 Simplifying x = 6.642183308Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.357816692, 6.642183308}
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