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Simplifying x2 + 9x + -116 = 0 Reorder the terms: -116 + 9x + x2 = 0 Solving -116 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '116' to each side of the equation. -116 + 9x + 116 + x2 = 0 + 116 Reorder the terms: -116 + 116 + 9x + x2 = 0 + 116 Combine like terms: -116 + 116 = 0 0 + 9x + x2 = 0 + 116 9x + x2 = 0 + 116 Combine like terms: 0 + 116 = 116 9x + x2 = 116 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 116 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 116 + 20.25 Combine like terms: 116 + 20.25 = 136.25 20.25 + 9x + x2 = 136.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 136.25 Calculate the square root of the right side: 11.67261753 Break this problem into two subproblems by setting (x + 4.5) equal to 11.67261753 and -11.67261753.Subproblem 1
x + 4.5 = 11.67261753 Simplifying x + 4.5 = 11.67261753 Reorder the terms: 4.5 + x = 11.67261753 Solving 4.5 + x = 11.67261753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 11.67261753 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 11.67261753 + -4.5 x = 11.67261753 + -4.5 Combine like terms: 11.67261753 + -4.5 = 7.17261753 x = 7.17261753 Simplifying x = 7.17261753Subproblem 2
x + 4.5 = -11.67261753 Simplifying x + 4.5 = -11.67261753 Reorder the terms: 4.5 + x = -11.67261753 Solving 4.5 + x = -11.67261753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -11.67261753 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -11.67261753 + -4.5 x = -11.67261753 + -4.5 Combine like terms: -11.67261753 + -4.5 = -16.17261753 x = -16.17261753 Simplifying x = -16.17261753Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.17261753, -16.17261753}
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