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Simplifying x2 + 5x + -131 = 0 Reorder the terms: -131 + 5x + x2 = 0 Solving -131 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '131' to each side of the equation. -131 + 5x + 131 + x2 = 0 + 131 Reorder the terms: -131 + 131 + 5x + x2 = 0 + 131 Combine like terms: -131 + 131 = 0 0 + 5x + x2 = 0 + 131 5x + x2 = 0 + 131 Combine like terms: 0 + 131 = 131 5x + x2 = 131 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 = 131 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 131 + 6.25 Combine like terms: 131 + 6.25 = 137.25 6.25 + 5x + x2 = 137.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 137.25 Calculate the square root of the right side: 11.715374514 Break this problem into two subproblems by setting (x + 2.5) equal to 11.715374514 and -11.715374514.Subproblem 1
x + 2.5 = 11.715374514 Simplifying x + 2.5 = 11.715374514 Reorder the terms: 2.5 + x = 11.715374514 Solving 2.5 + x = 11.715374514 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 = 11.715374514 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 11.715374514 + -2.5 x = 11.715374514 + -2.5 Combine like terms: 11.715374514 + -2.5 = 9.215374514 x = 9.215374514 Simplifying x = 9.215374514Subproblem 2
x + 2.5 = -11.715374514 Simplifying x + 2.5 = -11.715374514 Reorder the terms: 2.5 + x = -11.715374514 Solving 2.5 + x = -11.715374514 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 = -11.715374514 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -11.715374514 + -2.5 x = -11.715374514 + -2.5 Combine like terms: -11.715374514 + -2.5 = -14.215374514 x = -14.215374514 Simplifying x = -14.215374514Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.215374514, -14.215374514}
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