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Simplifying 2x2 + -6x + -115 = 0 Reorder the terms: -115 + -6x + 2x2 = 0 Solving -115 + -6x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -57.5 + -3x + x2 = 0 Move the constant term to the right: Add '57.5' to each side of the equation. -57.5 + -3x + 57.5 + x2 = 0 + 57.5 Reorder the terms: -57.5 + 57.5 + -3x + x2 = 0 + 57.5 Combine like terms: -57.5 + 57.5 = 0.0 0.0 + -3x + x2 = 0 + 57.5 -3x + x2 = 0 + 57.5 Combine like terms: 0 + 57.5 = 57.5 -3x + x2 = 57.5 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 57.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 57.5 + 2.25 Combine like terms: 57.5 + 2.25 = 59.75 2.25 + -3x + x2 = 59.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 59.75 Calculate the square root of the right side: 7.729812417 Break this problem into two subproblems by setting (x + -1.5) equal to 7.729812417 and -7.729812417.Subproblem 1
x + -1.5 = 7.729812417 Simplifying x + -1.5 = 7.729812417 Reorder the terms: -1.5 + x = 7.729812417 Solving -1.5 + x = 7.729812417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 7.729812417 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 7.729812417 + 1.5 x = 7.729812417 + 1.5 Combine like terms: 7.729812417 + 1.5 = 9.229812417 x = 9.229812417 Simplifying x = 9.229812417Subproblem 2
x + -1.5 = -7.729812417 Simplifying x + -1.5 = -7.729812417 Reorder the terms: -1.5 + x = -7.729812417 Solving -1.5 + x = -7.729812417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -7.729812417 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -7.729812417 + 1.5 x = -7.729812417 + 1.5 Combine like terms: -7.729812417 + 1.5 = -6.229812417 x = -6.229812417 Simplifying x = -6.229812417Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.229812417, -6.229812417}
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