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Simplifying x2 + -37x + 150 = 0 Reorder the terms: 150 + -37x + x2 = 0 Solving 150 + -37x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-150' to each side of the equation. 150 + -37x + -150 + x2 = 0 + -150 Reorder the terms: 150 + -150 + -37x + x2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + -37x + x2 = 0 + -150 -37x + x2 = 0 + -150 Combine like terms: 0 + -150 = -150 -37x + x2 = -150 The x term is -37x. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37x + 342.25 + x2 = -150 + 342.25 Reorder the terms: 342.25 + -37x + x2 = -150 + 342.25 Combine like terms: -150 + 342.25 = 192.25 342.25 + -37x + x2 = 192.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 192.25 Calculate the square root of the right side: 13.865424624 Break this problem into two subproblems by setting (x + -18.5) equal to 13.865424624 and -13.865424624.Subproblem 1
x + -18.5 = 13.865424624 Simplifying x + -18.5 = 13.865424624 Reorder the terms: -18.5 + x = 13.865424624 Solving -18.5 + x = 13.865424624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = 13.865424624 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 13.865424624 + 18.5 x = 13.865424624 + 18.5 Combine like terms: 13.865424624 + 18.5 = 32.365424624 x = 32.365424624 Simplifying x = 32.365424624Subproblem 2
x + -18.5 = -13.865424624 Simplifying x + -18.5 = -13.865424624 Reorder the terms: -18.5 + x = -13.865424624 Solving -18.5 + x = -13.865424624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = -13.865424624 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -13.865424624 + 18.5 x = -13.865424624 + 18.5 Combine like terms: -13.865424624 + 18.5 = 4.634575376 x = 4.634575376 Simplifying x = 4.634575376Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.365424624, 4.634575376}
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