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Simplifying x2 + 23x + -135 = 0 Reorder the terms: -135 + 23x + x2 = 0 Solving -135 + 23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '135' to each side of the equation. -135 + 23x + 135 + x2 = 0 + 135 Reorder the terms: -135 + 135 + 23x + x2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + 23x + x2 = 0 + 135 23x + x2 = 0 + 135 Combine like terms: 0 + 135 = 135 23x + x2 = 135 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = 135 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 135 + 132.25 Combine like terms: 135 + 132.25 = 267.25 132.25 + 23x + x2 = 267.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 267.25 Calculate the square root of the right side: 16.347782724 Break this problem into two subproblems by setting (x + 11.5) equal to 16.347782724 and -16.347782724.Subproblem 1
x + 11.5 = 16.347782724 Simplifying x + 11.5 = 16.347782724 Reorder the terms: 11.5 + x = 16.347782724 Solving 11.5 + x = 16.347782724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 16.347782724 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 16.347782724 + -11.5 x = 16.347782724 + -11.5 Combine like terms: 16.347782724 + -11.5 = 4.847782724 x = 4.847782724 Simplifying x = 4.847782724Subproblem 2
x + 11.5 = -16.347782724 Simplifying x + 11.5 = -16.347782724 Reorder the terms: 11.5 + x = -16.347782724 Solving 11.5 + x = -16.347782724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -16.347782724 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -16.347782724 + -11.5 x = -16.347782724 + -11.5 Combine like terms: -16.347782724 + -11.5 = -27.847782724 x = -27.847782724 Simplifying x = -27.847782724Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.847782724, -27.847782724}
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