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Simplifying x2 + 5x + -133 = 0 Reorder the terms: -133 + 5x + x2 = 0 Solving -133 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '133' to each side of the equation. -133 + 5x + 133 + x2 = 0 + 133 Reorder the terms: -133 + 133 + 5x + x2 = 0 + 133 Combine like terms: -133 + 133 = 0 0 + 5x + x2 = 0 + 133 5x + x2 = 0 + 133 Combine like terms: 0 + 133 = 133 5x + x2 = 133 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 = 133 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 133 + 6.25 Combine like terms: 133 + 6.25 = 139.25 6.25 + 5x + x2 = 139.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 139.25 Calculate the square root of the right side: 11.800423721 Break this problem into two subproblems by setting (x + 2.5) equal to 11.800423721 and -11.800423721.Subproblem 1
x + 2.5 = 11.800423721 Simplifying x + 2.5 = 11.800423721 Reorder the terms: 2.5 + x = 11.800423721 Solving 2.5 + x = 11.800423721 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 = 11.800423721 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 11.800423721 + -2.5 x = 11.800423721 + -2.5 Combine like terms: 11.800423721 + -2.5 = 9.300423721 x = 9.300423721 Simplifying x = 9.300423721Subproblem 2
x + 2.5 = -11.800423721 Simplifying x + 2.5 = -11.800423721 Reorder the terms: 2.5 + x = -11.800423721 Solving 2.5 + x = -11.800423721 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 = -11.800423721 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -11.800423721 + -2.5 x = -11.800423721 + -2.5 Combine like terms: -11.800423721 + -2.5 = -14.300423721 x = -14.300423721 Simplifying x = -14.300423721Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.300423721, -14.300423721}
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