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Simplifying x2 + 9x + -31 = 0 Reorder the terms: -31 + 9x + x2 = 0 Solving -31 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 9x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 9x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 9x + x2 = 0 + 31 9x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 9x + x2 = 31 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 = 31 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 31 + 20.25 Combine like terms: 31 + 20.25 = 51.25 20.25 + 9x + x2 = 51.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + 4.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + 4.5 = 7.158910532 Simplifying x + 4.5 = 7.158910532 Reorder the terms: 4.5 + x = 7.158910532 Solving 4.5 + x = 7.158910532 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 = 7.158910532 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 7.158910532 + -4.5 x = 7.158910532 + -4.5 Combine like terms: 7.158910532 + -4.5 = 2.658910532 x = 2.658910532 Simplifying x = 2.658910532Subproblem 2
x + 4.5 = -7.158910532 Simplifying x + 4.5 = -7.158910532 Reorder the terms: 4.5 + x = -7.158910532 Solving 4.5 + x = -7.158910532 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 = -7.158910532 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -7.158910532 + -4.5 x = -7.158910532 + -4.5 Combine like terms: -7.158910532 + -4.5 = -11.658910532 x = -11.658910532 Simplifying x = -11.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.658910532, -11.658910532}
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