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Simplifying x2 + x + -4088 = 0 Reorder the terms: -4088 + x + x2 = 0 Solving -4088 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4088' to each side of the equation. -4088 + x + 4088 + x2 = 0 + 4088 Reorder the terms: -4088 + 4088 + x + x2 = 0 + 4088 Combine like terms: -4088 + 4088 = 0 0 + x + x2 = 0 + 4088 x + x2 = 0 + 4088 Combine like terms: 0 + 4088 = 4088 x + x2 = 4088 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 4088 + 0.25 Reorder the terms: 0.25 + x + x2 = 4088 + 0.25 Combine like terms: 4088 + 0.25 = 4088.25 0.25 + x + x2 = 4088.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4088.25 Calculate the square root of the right side: 63.939424458 Break this problem into two subproblems by setting (x + 0.5) equal to 63.939424458 and -63.939424458.Subproblem 1
x + 0.5 = 63.939424458 Simplifying x + 0.5 = 63.939424458 Reorder the terms: 0.5 + x = 63.939424458 Solving 0.5 + x = 63.939424458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 63.939424458 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 63.939424458 + -0.5 x = 63.939424458 + -0.5 Combine like terms: 63.939424458 + -0.5 = 63.439424458 x = 63.439424458 Simplifying x = 63.439424458Subproblem 2
x + 0.5 = -63.939424458 Simplifying x + 0.5 = -63.939424458 Reorder the terms: 0.5 + x = -63.939424458 Solving 0.5 + x = -63.939424458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -63.939424458 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -63.939424458 + -0.5 x = -63.939424458 + -0.5 Combine like terms: -63.939424458 + -0.5 = -64.439424458 x = -64.439424458 Simplifying x = -64.439424458Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.439424458, -64.439424458}
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