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Simplifying x2 + 5x + 6.25 = 61.25 Reorder the terms: 6.25 + 5x + x2 = 61.25 Solving 6.25 + 5x + x2 = 61.25 Solving for variable 'x'. Reorder the terms: 6.25 + -61.25 + 5x + x2 = 61.25 + -61.25 Combine like terms: 6.25 + -61.25 = -55 -55 + 5x + x2 = 61.25 + -61.25 Combine like terms: 61.25 + -61.25 = 0.00 -55 + 5x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 5x + 55 + x2 = 0.00 + 55 Reorder the terms: -55 + 55 + 5x + x2 = 0.00 + 55 Combine like terms: -55 + 55 = 0 0 + 5x + x2 = 0.00 + 55 5x + x2 = 0.00 + 55 Combine like terms: 0.00 + 55 = 55 5x + x2 = 55 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 55 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 55 + 6.25 Combine like terms: 55 + 6.25 = 61.25 6.25 + 5x + x2 = 61.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 61.25 Calculate the square root of the right side: 7.826237921 Break this problem into two subproblems by setting (x + 2.5) equal to 7.826237921 and -7.826237921.Subproblem 1
x + 2.5 = 7.826237921 Simplifying x + 2.5 = 7.826237921 Reorder the terms: 2.5 + x = 7.826237921 Solving 2.5 + x = 7.826237921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 7.826237921 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 7.826237921 + -2.5 x = 7.826237921 + -2.5 Combine like terms: 7.826237921 + -2.5 = 5.326237921 x = 5.326237921 Simplifying x = 5.326237921Subproblem 2
x + 2.5 = -7.826237921 Simplifying x + 2.5 = -7.826237921 Reorder the terms: 2.5 + x = -7.826237921 Solving 2.5 + x = -7.826237921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -7.826237921 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -7.826237921 + -2.5 x = -7.826237921 + -2.5 Combine like terms: -7.826237921 + -2.5 = -10.326237921 x = -10.326237921 Simplifying x = -10.326237921Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.326237921, -10.326237921}
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