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Simplifying x2 + -155x + (2135.71) = 0 x2 + -155x + 2135.71 = 0 Reorder the terms: 2135.71 + -155x + x2 = 0 Solving 2135.71 + -155x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2135.71' to each side of the equation. 2135.71 + -155x + -2135.71 + x2 = 0 + -2135.71 Reorder the terms: 2135.71 + -2135.71 + -155x + x2 = 0 + -2135.71 Combine like terms: 2135.71 + -2135.71 = 0.00 0.00 + -155x + x2 = 0 + -2135.71 -155x + x2 = 0 + -2135.71 Combine like terms: 0 + -2135.71 = -2135.71 -155x + x2 = -2135.71 The x term is -155x. Take half its coefficient (-77.5). Square it (6006.25) and add it to both sides. Add '6006.25' to each side of the equation. -155x + 6006.25 + x2 = -2135.71 + 6006.25 Reorder the terms: 6006.25 + -155x + x2 = -2135.71 + 6006.25 Combine like terms: -2135.71 + 6006.25 = 3870.54 6006.25 + -155x + x2 = 3870.54 Factor a perfect square on the left side: (x + -77.5)(x + -77.5) = 3870.54 Calculate the square root of the right side: 62.213664094 Break this problem into two subproblems by setting (x + -77.5) equal to 62.213664094 and -62.213664094.Subproblem 1
x + -77.5 = 62.213664094 Simplifying x + -77.5 = 62.213664094 Reorder the terms: -77.5 + x = 62.213664094 Solving -77.5 + x = 62.213664094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '77.5' to each side of the equation. -77.5 + 77.5 + x = 62.213664094 + 77.5 Combine like terms: -77.5 + 77.5 = 0.0 0.0 + x = 62.213664094 + 77.5 x = 62.213664094 + 77.5 Combine like terms: 62.213664094 + 77.5 = 139.713664094 x = 139.713664094 Simplifying x = 139.713664094Subproblem 2
x + -77.5 = -62.213664094 Simplifying x + -77.5 = -62.213664094 Reorder the terms: -77.5 + x = -62.213664094 Solving -77.5 + x = -62.213664094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '77.5' to each side of the equation. -77.5 + 77.5 + x = -62.213664094 + 77.5 Combine like terms: -77.5 + 77.5 = 0.0 0.0 + x = -62.213664094 + 77.5 x = -62.213664094 + 77.5 Combine like terms: -62.213664094 + 77.5 = 15.286335906 x = 15.286335906 Simplifying x = 15.286335906Solution
The solution to the problem is based on the solutions from the subproblems. x = {139.713664094, 15.286335906}
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