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Simplifying x2 + 16x + 31 = 0 Reorder the terms: 31 + 16x + x2 = 0 Solving 31 + 16x + 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 + 16x + -31 + x2 = 0 + -31 Reorder the terms: 31 + -31 + 16x + x2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 16x + x2 = 0 + -31 16x + x2 = 0 + -31 Combine like terms: 0 + -31 = -31 16x + x2 = -31 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -31 + 64 Reorder the terms: 64 + 16x + x2 = -31 + 64 Combine like terms: -31 + 64 = 33 64 + 16x + x2 = 33 Factor a perfect square on the left side: (x + 8)(x + 8) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + 8) equal to 5.744562647 and -5.744562647.Subproblem 1
x + 8 = 5.744562647 Simplifying x + 8 = 5.744562647 Reorder the terms: 8 + x = 5.744562647 Solving 8 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 5.744562647 + -8 Combine like terms: 8 + -8 = 0 0 + x = 5.744562647 + -8 x = 5.744562647 + -8 Combine like terms: 5.744562647 + -8 = -2.255437353 x = -2.255437353 Simplifying x = -2.255437353Subproblem 2
x + 8 = -5.744562647 Simplifying x + 8 = -5.744562647 Reorder the terms: 8 + x = -5.744562647 Solving 8 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -5.744562647 + -8 Combine like terms: 8 + -8 = 0 0 + x = -5.744562647 + -8 x = -5.744562647 + -8 Combine like terms: -5.744562647 + -8 = -13.744562647 x = -13.744562647 Simplifying x = -13.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.255437353, -13.744562647}
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