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Simplifying x2 + 16x + -16 = 0 Reorder the terms: -16 + 16x + x2 = 0 Solving -16 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 16x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 16x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 16x + x2 = 0 + 16 16x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 16x + x2 = 16 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 = 16 + 64 Reorder the terms: 64 + 16x + x2 = 16 + 64 Combine like terms: 16 + 64 = 80 64 + 16x + x2 = 80 Factor a perfect square on the left side: (x + 8)(x + 8) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + 8) equal to 8.94427191 and -8.94427191.Subproblem 1
x + 8 = 8.94427191 Simplifying x + 8 = 8.94427191 Reorder the terms: 8 + x = 8.94427191 Solving 8 + x = 8.94427191 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 = 8.94427191 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.94427191 + -8 x = 8.94427191 + -8 Combine like terms: 8.94427191 + -8 = 0.94427191 x = 0.94427191 Simplifying x = 0.94427191Subproblem 2
x + 8 = -8.94427191 Simplifying x + 8 = -8.94427191 Reorder the terms: 8 + x = -8.94427191 Solving 8 + x = -8.94427191 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 = -8.94427191 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.94427191 + -8 x = -8.94427191 + -8 Combine like terms: -8.94427191 + -8 = -16.94427191 x = -16.94427191 Simplifying x = -16.94427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.94427191, -16.94427191}
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