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Simplifying 480x + -2x2 + -240 = x Reorder the terms: -240 + 480x + -2x2 = x Solving -240 + 480x + -2x2 = x Solving for variable 'x'. Reorder the terms: -240 + 480x + -1x + -2x2 = x + -1x Combine like terms: 480x + -1x = 479x -240 + 479x + -2x2 = x + -1x Combine like terms: x + -1x = 0 -240 + 479x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 120 + -239.5x + x2 = 0 Move the constant term to the right: Add '-120' to each side of the equation. 120 + -239.5x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + -239.5x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + -239.5x + x2 = 0 + -120 -239.5x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 -239.5x + x2 = -120 The x term is -239.5x. Take half its coefficient (-119.75). Square it (14340.0625) and add it to both sides. Add '14340.0625' to each side of the equation. -239.5x + 14340.0625 + x2 = -120 + 14340.0625 Reorder the terms: 14340.0625 + -239.5x + x2 = -120 + 14340.0625 Combine like terms: -120 + 14340.0625 = 14220.0625 14340.0625 + -239.5x + x2 = 14220.0625 Factor a perfect square on the left side: (x + -119.75)(x + -119.75) = 14220.0625 Calculate the square root of the right side: 119.247903546 Break this problem into two subproblems by setting (x + -119.75) equal to 119.247903546 and -119.247903546.Subproblem 1
x + -119.75 = 119.247903546 Simplifying x + -119.75 = 119.247903546 Reorder the terms: -119.75 + x = 119.247903546 Solving -119.75 + x = 119.247903546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '119.75' to each side of the equation. -119.75 + 119.75 + x = 119.247903546 + 119.75 Combine like terms: -119.75 + 119.75 = 0.00 0.00 + x = 119.247903546 + 119.75 x = 119.247903546 + 119.75 Combine like terms: 119.247903546 + 119.75 = 238.997903546 x = 238.997903546 Simplifying x = 238.997903546Subproblem 2
x + -119.75 = -119.247903546 Simplifying x + -119.75 = -119.247903546 Reorder the terms: -119.75 + x = -119.247903546 Solving -119.75 + x = -119.247903546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '119.75' to each side of the equation. -119.75 + 119.75 + x = -119.247903546 + 119.75 Combine like terms: -119.75 + 119.75 = 0.00 0.00 + x = -119.247903546 + 119.75 x = -119.247903546 + 119.75 Combine like terms: -119.247903546 + 119.75 = 0.502096454 x = 0.502096454 Simplifying x = 0.502096454Solution
The solution to the problem is based on the solutions from the subproblems. x = {238.997903546, 0.502096454}
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