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Simplifying 2x + 120 = x2 + -6x Reorder the terms: 120 + 2x = x2 + -6x Reorder the terms: 120 + 2x = -6x + x2 Solving 120 + 2x = -6x + x2 Solving for variable 'x'. Combine like terms: 2x + 6x = 8x 120 + 8x + -1x2 = -6x + x2 + 6x + -1x2 Reorder the terms: 120 + 8x + -1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 120 + 8x + -1x2 = 0 + x2 + -1x2 120 + 8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 120 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -120 + -8x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + -8x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + -8x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -8x + x2 = 0 + 120 -8x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 -8x + x2 = 120 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 120 + 16 Reorder the terms: 16 + -8x + x2 = 120 + 16 Combine like terms: 120 + 16 = 136 16 + -8x + x2 = 136 Factor a perfect square on the left side: (x + -4)(x + -4) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (x + -4) equal to 11.66190379 and -11.66190379.Subproblem 1
x + -4 = 11.66190379 Simplifying x + -4 = 11.66190379 Reorder the terms: -4 + x = 11.66190379 Solving -4 + x = 11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 11.66190379 + 4 Combine like terms: -4 + 4 = 0 0 + x = 11.66190379 + 4 x = 11.66190379 + 4 Combine like terms: 11.66190379 + 4 = 15.66190379 x = 15.66190379 Simplifying x = 15.66190379Subproblem 2
x + -4 = -11.66190379 Simplifying x + -4 = -11.66190379 Reorder the terms: -4 + x = -11.66190379 Solving -4 + x = -11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -11.66190379 + 4 Combine like terms: -4 + 4 = 0 0 + x = -11.66190379 + 4 x = -11.66190379 + 4 Combine like terms: -11.66190379 + 4 = -7.66190379 x = -7.66190379 Simplifying x = -7.66190379Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.66190379, -7.66190379}
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