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Simplifying x2 + -31x + -234 = 0 Reorder the terms: -234 + -31x + x2 = 0 Solving -234 + -31x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '234' to each side of the equation. -234 + -31x + 234 + x2 = 0 + 234 Reorder the terms: -234 + 234 + -31x + x2 = 0 + 234 Combine like terms: -234 + 234 = 0 0 + -31x + x2 = 0 + 234 -31x + x2 = 0 + 234 Combine like terms: 0 + 234 = 234 -31x + x2 = 234 The x term is -31x. Take half its coefficient (-15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. -31x + 240.25 + x2 = 234 + 240.25 Reorder the terms: 240.25 + -31x + x2 = 234 + 240.25 Combine like terms: 234 + 240.25 = 474.25 240.25 + -31x + x2 = 474.25 Factor a perfect square on the left side: (x + -15.5)(x + -15.5) = 474.25 Calculate the square root of the right side: 21.77728174 Break this problem into two subproblems by setting (x + -15.5) equal to 21.77728174 and -21.77728174.Subproblem 1
x + -15.5 = 21.77728174 Simplifying x + -15.5 = 21.77728174 Reorder the terms: -15.5 + x = 21.77728174 Solving -15.5 + x = 21.77728174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = 21.77728174 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = 21.77728174 + 15.5 x = 21.77728174 + 15.5 Combine like terms: 21.77728174 + 15.5 = 37.27728174 x = 37.27728174 Simplifying x = 37.27728174Subproblem 2
x + -15.5 = -21.77728174 Simplifying x + -15.5 = -21.77728174 Reorder the terms: -15.5 + x = -21.77728174 Solving -15.5 + x = -21.77728174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + x = -21.77728174 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = -21.77728174 + 15.5 x = -21.77728174 + 15.5 Combine like terms: -21.77728174 + 15.5 = -6.27728174 x = -6.27728174 Simplifying x = -6.27728174Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.27728174, -6.27728174}
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