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Simplifying x2 + 8x = 120 Reorder the terms: 8x + x2 = 120 Solving 8x + x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + 8x + x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 8x + x2 = 0 Begin completing the square. 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 = 7.66190379 x = 7.66190379 Simplifying x = 7.66190379Subproblem 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 = -15.66190379 x = -15.66190379 Simplifying x = -15.66190379Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.66190379, -15.66190379}
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