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Simplifying 120 + 40x + x2 = 0 Solving 120 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-120' to each side of the equation. 120 + 40x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + 40x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + 40x + x2 = 0 + -120 40x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 40x + x2 = -120 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = -120 + 400 Reorder the terms: 400 + 40x + x2 = -120 + 400 Combine like terms: -120 + 400 = 280 400 + 40x + x2 = 280 Factor a perfect square on the left side: (x + 20)(x + 20) = 280 Calculate the square root of the right side: 16.733200531 Break this problem into two subproblems by setting (x + 20) equal to 16.733200531 and -16.733200531.Subproblem 1
x + 20 = 16.733200531 Simplifying x + 20 = 16.733200531 Reorder the terms: 20 + x = 16.733200531 Solving 20 + x = 16.733200531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 16.733200531 + -20 Combine like terms: 20 + -20 = 0 0 + x = 16.733200531 + -20 x = 16.733200531 + -20 Combine like terms: 16.733200531 + -20 = -3.266799469 x = -3.266799469 Simplifying x = -3.266799469Subproblem 2
x + 20 = -16.733200531 Simplifying x + 20 = -16.733200531 Reorder the terms: 20 + x = -16.733200531 Solving 20 + x = -16.733200531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -16.733200531 + -20 Combine like terms: 20 + -20 = 0 0 + x = -16.733200531 + -20 x = -16.733200531 + -20 Combine like terms: -16.733200531 + -20 = -36.733200531 x = -36.733200531 Simplifying x = -36.733200531Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.266799469, -36.733200531}
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