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Simplifying x2 + -12x + -31 = 0 Reorder the terms: -31 + -12x + x2 = 0 Solving -31 + -12x + 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 + -12x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + -12x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -12x + x2 = 0 + 31 -12x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 -12x + x2 = 31 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 31 + 36 Reorder the terms: 36 + -12x + x2 = 31 + 36 Combine like terms: 31 + 36 = 67 36 + -12x + x2 = 67 Factor a perfect square on the left side: (x + -6)(x + -6) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + -6) equal to 8.185352772 and -8.185352772.Subproblem 1
x + -6 = 8.185352772 Simplifying x + -6 = 8.185352772 Reorder the terms: -6 + x = 8.185352772 Solving -6 + x = 8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 8.185352772 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.185352772 + 6 x = 8.185352772 + 6 Combine like terms: 8.185352772 + 6 = 14.185352772 x = 14.185352772 Simplifying x = 14.185352772Subproblem 2
x + -6 = -8.185352772 Simplifying x + -6 = -8.185352772 Reorder the terms: -6 + x = -8.185352772 Solving -6 + x = -8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -8.185352772 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.185352772 + 6 x = -8.185352772 + 6 Combine like terms: -8.185352772 + 6 = -2.185352772 x = -2.185352772 Simplifying x = -2.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.185352772, -2.185352772}
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