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Simplifying -1x2 + -12x = -87 Reorder the terms: -12x + -1x2 = -87 Solving -12x + -1x2 = -87 Solving for variable 'x'. Reorder the terms: 87 + -12x + -1x2 = -87 + 87 Combine like terms: -87 + 87 = 0 87 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -87 + 12x + x2 = 0 Move the constant term to the right: Add '87' to each side of the equation. -87 + 12x + 87 + x2 = 0 + 87 Reorder the terms: -87 + 87 + 12x + x2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + 12x + x2 = 0 + 87 12x + x2 = 0 + 87 Combine like terms: 0 + 87 = 87 12x + x2 = 87 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 87 + 36 Reorder the terms: 36 + 12x + x2 = 87 + 36 Combine like terms: 87 + 36 = 123 36 + 12x + x2 = 123 Factor a perfect square on the left side: (x + 6)(x + 6) = 123 Calculate the square root of the right side: 11.090536506 Break this problem into two subproblems by setting (x + 6) equal to 11.090536506 and -11.090536506.Subproblem 1
x + 6 = 11.090536506 Simplifying x + 6 = 11.090536506 Reorder the terms: 6 + x = 11.090536506 Solving 6 + x = 11.090536506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 11.090536506 + -6 Combine like terms: 6 + -6 = 0 0 + x = 11.090536506 + -6 x = 11.090536506 + -6 Combine like terms: 11.090536506 + -6 = 5.090536506 x = 5.090536506 Simplifying x = 5.090536506Subproblem 2
x + 6 = -11.090536506 Simplifying x + 6 = -11.090536506 Reorder the terms: 6 + x = -11.090536506 Solving 6 + x = -11.090536506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -11.090536506 + -6 Combine like terms: 6 + -6 = 0 0 + x = -11.090536506 + -6 x = -11.090536506 + -6 Combine like terms: -11.090536506 + -6 = -17.090536506 x = -17.090536506 Simplifying x = -17.090536506Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.090536506, -17.090536506}
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