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Simplifying x2 + 16x + -67 = 0 Reorder the terms: -67 + 16x + x2 = 0 Solving -67 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '67' to each side of the equation. -67 + 16x + 67 + x2 = 0 + 67 Reorder the terms: -67 + 67 + 16x + x2 = 0 + 67 Combine like terms: -67 + 67 = 0 0 + 16x + x2 = 0 + 67 16x + x2 = 0 + 67 Combine like terms: 0 + 67 = 67 16x + x2 = 67 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 = 67 + 64 Reorder the terms: 64 + 16x + x2 = 67 + 64 Combine like terms: 67 + 64 = 131 64 + 16x + x2 = 131 Factor a perfect square on the left side: (x + 8)(x + 8) = 131 Calculate the square root of the right side: 11.445523142 Break this problem into two subproblems by setting (x + 8) equal to 11.445523142 and -11.445523142.Subproblem 1
x + 8 = 11.445523142 Simplifying x + 8 = 11.445523142 Reorder the terms: 8 + x = 11.445523142 Solving 8 + x = 11.445523142 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 = 11.445523142 + -8 Combine like terms: 8 + -8 = 0 0 + x = 11.445523142 + -8 x = 11.445523142 + -8 Combine like terms: 11.445523142 + -8 = 3.445523142 x = 3.445523142 Simplifying x = 3.445523142Subproblem 2
x + 8 = -11.445523142 Simplifying x + 8 = -11.445523142 Reorder the terms: 8 + x = -11.445523142 Solving 8 + x = -11.445523142 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 = -11.445523142 + -8 Combine like terms: 8 + -8 = 0 0 + x = -11.445523142 + -8 x = -11.445523142 + -8 Combine like terms: -11.445523142 + -8 = -19.445523142 x = -19.445523142 Simplifying x = -19.445523142Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.445523142, -19.445523142}
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