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Simplifying x2 + x + -62.5 = 0 Reorder the terms: -62.5 + x + x2 = 0 Solving -62.5 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '62.5' to each side of the equation. -62.5 + x + 62.5 + x2 = 0 + 62.5 Reorder the terms: -62.5 + 62.5 + x + x2 = 0 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + x + x2 = 0 + 62.5 x + x2 = 0 + 62.5 Combine like terms: 0 + 62.5 = 62.5 x + x2 = 62.5 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 = 62.5 + 0.25 Reorder the terms: 0.25 + x + x2 = 62.5 + 0.25 Combine like terms: 62.5 + 0.25 = 62.75 0.25 + x + x2 = 62.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 62.75 Calculate the square root of the right side: 7.921489759 Break this problem into two subproblems by setting (x + 0.5) equal to 7.921489759 and -7.921489759.Subproblem 1
x + 0.5 = 7.921489759 Simplifying x + 0.5 = 7.921489759 Reorder the terms: 0.5 + x = 7.921489759 Solving 0.5 + x = 7.921489759 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 = 7.921489759 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.921489759 + -0.5 x = 7.921489759 + -0.5 Combine like terms: 7.921489759 + -0.5 = 7.421489759 x = 7.421489759 Simplifying x = 7.421489759Subproblem 2
x + 0.5 = -7.921489759 Simplifying x + 0.5 = -7.921489759 Reorder the terms: 0.5 + x = -7.921489759 Solving 0.5 + x = -7.921489759 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 = -7.921489759 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.921489759 + -0.5 x = -7.921489759 + -0.5 Combine like terms: -7.921489759 + -0.5 = -8.421489759 x = -8.421489759 Simplifying x = -8.421489759Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.421489759, -8.421489759}
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