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Simplifying -1x2 + 8x + 31 = 0 Reorder the terms: 31 + 8x + -1x2 = 0 Solving 31 + 8x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -31 + -8x + x2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + -8x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + -8x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -8x + x2 = 0 + 31 -8x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 -8x + x2 = 31 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 31 + 16 Reorder the terms: 16 + -8x + x2 = 31 + 16 Combine like terms: 31 + 16 = 47 16 + -8x + x2 = 47 Factor a perfect square on the left side: (x + -4)(x + -4) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x + -4) equal to 6.8556546 and -6.8556546.Subproblem 1
x + -4 = 6.8556546 Simplifying x + -4 = 6.8556546 Reorder the terms: -4 + x = 6.8556546 Solving -4 + x = 6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 6.8556546 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.8556546 + 4 x = 6.8556546 + 4 Combine like terms: 6.8556546 + 4 = 10.8556546 x = 10.8556546 Simplifying x = 10.8556546Subproblem 2
x + -4 = -6.8556546 Simplifying x + -4 = -6.8556546 Reorder the terms: -4 + x = -6.8556546 Solving -4 + x = -6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -6.8556546 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.8556546 + 4 x = -6.8556546 + 4 Combine like terms: -6.8556546 + 4 = -2.8556546 x = -2.8556546 Simplifying x = -2.8556546Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.8556546, -2.8556546}
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