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Simplifying x^{2}+ 5x + -59 = 0 Reorder the terms: -59 + 5x + x^{2}= 0 Solving -59 + 5x + x^{2}= 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + 5x + 59 + x^{2}= 0 + 59 Reorder the terms: -59 + 59 + 5x + x^{2}= 0 + 59 Combine like terms: -59 + 59 = 0 0 + 5x + x^{2}= 0 + 59 5x + x^{2}= 0 + 59 Combine like terms: 0 + 59 = 59 5x + x^{2}= 59 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 + x^{2}= 59 + 6.25 Reorder the terms: 6.25 + 5x + x^{2}= 59 + 6.25 Combine like terms: 59 + 6.25 = 65.25 6.25 + 5x + x^{2}= 65.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 65.25 Calculate the square root of the right side: 8.077747211 Break this problem into two subproblems by setting (x + 2.5) equal to 8.077747211 and -8.077747211.## Subproblem 1

x + 2.5 = 8.077747211 Simplifying x + 2.5 = 8.077747211 Reorder the terms: 2.5 + x = 8.077747211 Solving 2.5 + x = 8.077747211 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 = 8.077747211 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 8.077747211 + -2.5 x = 8.077747211 + -2.5 Combine like terms: 8.077747211 + -2.5 = 5.577747211 x = 5.577747211 Simplifying x = 5.577747211## Subproblem 2

x + 2.5 = -8.077747211 Simplifying x + 2.5 = -8.077747211 Reorder the terms: 2.5 + x = -8.077747211 Solving 2.5 + x = -8.077747211 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 = -8.077747211 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -8.077747211 + -2.5 x = -8.077747211 + -2.5 Combine like terms: -8.077747211 + -2.5 = -10.577747211 x = -10.577747211 Simplifying x = -10.577747211## Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.577747211, -10.577747211}

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