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Simplifying -200x2 + 110x + 31 = 0 Reorder the terms: 31 + 110x + -200x2 = 0 Solving 31 + 110x + -200x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -200 the coefficient of the squared term: Divide each side by '-200'. -0.155 + -0.55x + x2 = 0 Move the constant term to the right: Add '0.155' to each side of the equation. -0.155 + -0.55x + 0.155 + x2 = 0 + 0.155 Reorder the terms: -0.155 + 0.155 + -0.55x + x2 = 0 + 0.155 Combine like terms: -0.155 + 0.155 = 0.000 0.000 + -0.55x + x2 = 0 + 0.155 -0.55x + x2 = 0 + 0.155 Combine like terms: 0 + 0.155 = 0.155 -0.55x + x2 = 0.155 The x term is -0.55x. Take half its coefficient (-0.275). Square it (0.075625) and add it to both sides. Add '0.075625' to each side of the equation. -0.55x + 0.075625 + x2 = 0.155 + 0.075625 Reorder the terms: 0.075625 + -0.55x + x2 = 0.155 + 0.075625 Combine like terms: 0.155 + 0.075625 = 0.230625 0.075625 + -0.55x + x2 = 0.230625 Factor a perfect square on the left side: (x + -0.275)(x + -0.275) = 0.230625 Calculate the square root of the right side: 0.480234318 Break this problem into two subproblems by setting (x + -0.275) equal to 0.480234318 and -0.480234318.Subproblem 1
x + -0.275 = 0.480234318 Simplifying x + -0.275 = 0.480234318 Reorder the terms: -0.275 + x = 0.480234318 Solving -0.275 + x = 0.480234318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + x = 0.480234318 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + x = 0.480234318 + 0.275 x = 0.480234318 + 0.275 Combine like terms: 0.480234318 + 0.275 = 0.755234318 x = 0.755234318 Simplifying x = 0.755234318Subproblem 2
x + -0.275 = -0.480234318 Simplifying x + -0.275 = -0.480234318 Reorder the terms: -0.275 + x = -0.480234318 Solving -0.275 + x = -0.480234318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + x = -0.480234318 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + x = -0.480234318 + 0.275 x = -0.480234318 + 0.275 Combine like terms: -0.480234318 + 0.275 = -0.205234318 x = -0.205234318 Simplifying x = -0.205234318Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.755234318, -0.205234318}
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