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Simplifying x2 + 5x + -118 = 0 Reorder the terms: -118 + 5x + x2 = 0 Solving -118 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '118' to each side of the equation. -118 + 5x + 118 + x2 = 0 + 118 Reorder the terms: -118 + 118 + 5x + x2 = 0 + 118 Combine like terms: -118 + 118 = 0 0 + 5x + x2 = 0 + 118 5x + x2 = 0 + 118 Combine like terms: 0 + 118 = 118 5x + x2 = 118 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 = 118 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 118 + 6.25 Combine like terms: 118 + 6.25 = 124.25 6.25 + 5x + x2 = 124.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 124.25 Calculate the square root of the right side: 11.146748405 Break this problem into two subproblems by setting (x + 2.5) equal to 11.146748405 and -11.146748405.Subproblem 1
x + 2.5 = 11.146748405 Simplifying x + 2.5 = 11.146748405 Reorder the terms: 2.5 + x = 11.146748405 Solving 2.5 + x = 11.146748405 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 = 11.146748405 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 11.146748405 + -2.5 x = 11.146748405 + -2.5 Combine like terms: 11.146748405 + -2.5 = 8.646748405 x = 8.646748405 Simplifying x = 8.646748405Subproblem 2
x + 2.5 = -11.146748405 Simplifying x + 2.5 = -11.146748405 Reorder the terms: 2.5 + x = -11.146748405 Solving 2.5 + x = -11.146748405 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 = -11.146748405 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -11.146748405 + -2.5 x = -11.146748405 + -2.5 Combine like terms: -11.146748405 + -2.5 = -13.646748405 x = -13.646748405 Simplifying x = -13.646748405Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.646748405, -13.646748405}
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