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Simplifying -1x2 + 6x + 120 = 0 Reorder the terms: 120 + 6x + -1x2 = 0 Solving 120 + 6x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -120 + -6x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + -6x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + -6x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -6x + x2 = 0 + 120 -6x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 -6x + x2 = 120 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 120 + 9 Reorder the terms: 9 + -6x + x2 = 120 + 9 Combine like terms: 120 + 9 = 129 9 + -6x + x2 = 129 Factor a perfect square on the left side: (x + -3)(x + -3) = 129 Calculate the square root of the right side: 11.357816692 Break this problem into two subproblems by setting (x + -3) equal to 11.357816692 and -11.357816692.Subproblem 1
x + -3 = 11.357816692 Simplifying x + -3 = 11.357816692 Reorder the terms: -3 + x = 11.357816692 Solving -3 + x = 11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 11.357816692 + 3 Combine like terms: -3 + 3 = 0 0 + x = 11.357816692 + 3 x = 11.357816692 + 3 Combine like terms: 11.357816692 + 3 = 14.357816692 x = 14.357816692 Simplifying x = 14.357816692Subproblem 2
x + -3 = -11.357816692 Simplifying x + -3 = -11.357816692 Reorder the terms: -3 + x = -11.357816692 Solving -3 + x = -11.357816692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -11.357816692 + 3 Combine like terms: -3 + 3 = 0 0 + x = -11.357816692 + 3 x = -11.357816692 + 3 Combine like terms: -11.357816692 + 3 = -8.357816692 x = -8.357816692 Simplifying x = -8.357816692Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.357816692, -8.357816692}
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