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Simplifying x2 + 16x + 64 = 8 Reorder the terms: 64 + 16x + x2 = 8 Solving 64 + 16x + x2 = 8 Solving for variable 'x'. Reorder the terms: 64 + -8 + 16x + x2 = 8 + -8 Combine like terms: 64 + -8 = 56 56 + 16x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 56 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + 16x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + 16x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + 16x + x2 = 0 + -56 16x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 16x + x2 = -56 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 = -56 + 64 Reorder the terms: 64 + 16x + x2 = -56 + 64 Combine like terms: -56 + 64 = 8 64 + 16x + x2 = 8 Factor a perfect square on the left side: (x + 8)(x + 8) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + 8) equal to 2.828427125 and -2.828427125.Subproblem 1
x + 8 = 2.828427125 Simplifying x + 8 = 2.828427125 Reorder the terms: 8 + x = 2.828427125 Solving 8 + x = 2.828427125 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 = 2.828427125 + -8 Combine like terms: 8 + -8 = 0 0 + x = 2.828427125 + -8 x = 2.828427125 + -8 Combine like terms: 2.828427125 + -8 = -5.171572875 x = -5.171572875 Simplifying x = -5.171572875Subproblem 2
x + 8 = -2.828427125 Simplifying x + 8 = -2.828427125 Reorder the terms: 8 + x = -2.828427125 Solving 8 + x = -2.828427125 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 = -2.828427125 + -8 Combine like terms: 8 + -8 = 0 0 + x = -2.828427125 + -8 x = -2.828427125 + -8 Combine like terms: -2.828427125 + -8 = -10.828427125 x = -10.828427125 Simplifying x = -10.828427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.171572875, -10.828427125}
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