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Simplifying (x2) + -128x + 240 = 0 x2 + -128x + 240 = 0 Reorder the terms: 240 + -128x + x2 = 0 Solving 240 + -128x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-240' to each side of the equation. 240 + -128x + -240 + x2 = 0 + -240 Reorder the terms: 240 + -240 + -128x + x2 = 0 + -240 Combine like terms: 240 + -240 = 0 0 + -128x + x2 = 0 + -240 -128x + x2 = 0 + -240 Combine like terms: 0 + -240 = -240 -128x + x2 = -240 The x term is -128x. Take half its coefficient (-64). Square it (4096) and add it to both sides. Add '4096' to each side of the equation. -128x + 4096 + x2 = -240 + 4096 Reorder the terms: 4096 + -128x + x2 = -240 + 4096 Combine like terms: -240 + 4096 = 3856 4096 + -128x + x2 = 3856 Factor a perfect square on the left side: (x + -64)(x + -64) = 3856 Calculate the square root of the right side: 62.096698785 Break this problem into two subproblems by setting (x + -64) equal to 62.096698785 and -62.096698785.Subproblem 1
x + -64 = 62.096698785 Simplifying x + -64 = 62.096698785 Reorder the terms: -64 + x = 62.096698785 Solving -64 + x = 62.096698785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '64' to each side of the equation. -64 + 64 + x = 62.096698785 + 64 Combine like terms: -64 + 64 = 0 0 + x = 62.096698785 + 64 x = 62.096698785 + 64 Combine like terms: 62.096698785 + 64 = 126.096698785 x = 126.096698785 Simplifying x = 126.096698785Subproblem 2
x + -64 = -62.096698785 Simplifying x + -64 = -62.096698785 Reorder the terms: -64 + x = -62.096698785 Solving -64 + x = -62.096698785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '64' to each side of the equation. -64 + 64 + x = -62.096698785 + 64 Combine like terms: -64 + 64 = 0 0 + x = -62.096698785 + 64 x = -62.096698785 + 64 Combine like terms: -62.096698785 + 64 = 1.903301215 x = 1.903301215 Simplifying x = 1.903301215Solution
The solution to the problem is based on the solutions from the subproblems. x = {126.096698785, 1.903301215}
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