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Simplifying x2 + 20x + -31 = 0 Reorder the terms: -31 + 20x + x2 = 0 Solving -31 + 20x + 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 + 20x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 20x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 20x + x2 = 0 + 31 20x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 20x + x2 = 31 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 31 + 100 Reorder the terms: 100 + 20x + x2 = 31 + 100 Combine like terms: 31 + 100 = 131 100 + 20x + x2 = 131 Factor a perfect square on the left side: (x + 10)(x + 10) = 131 Calculate the square root of the right side: 11.445523142 Break this problem into two subproblems by setting (x + 10) equal to 11.445523142 and -11.445523142.Subproblem 1
x + 10 = 11.445523142 Simplifying x + 10 = 11.445523142 Reorder the terms: 10 + x = 11.445523142 Solving 10 + x = 11.445523142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 11.445523142 + -10 Combine like terms: 10 + -10 = 0 0 + x = 11.445523142 + -10 x = 11.445523142 + -10 Combine like terms: 11.445523142 + -10 = 1.445523142 x = 1.445523142 Simplifying x = 1.445523142Subproblem 2
x + 10 = -11.445523142 Simplifying x + 10 = -11.445523142 Reorder the terms: 10 + x = -11.445523142 Solving 10 + x = -11.445523142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -11.445523142 + -10 Combine like terms: 10 + -10 = 0 0 + x = -11.445523142 + -10 x = -11.445523142 + -10 Combine like terms: -11.445523142 + -10 = -21.445523142 x = -21.445523142 Simplifying x = -21.445523142Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.445523142, -21.445523142}
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