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Simplifying x2 + 16x + 64 = 6 Reorder the terms: 64 + 16x + x2 = 6 Solving 64 + 16x + x2 = 6 Solving for variable 'x'. Reorder the terms: 64 + -6 + 16x + x2 = 6 + -6 Combine like terms: 64 + -6 = 58 58 + 16x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 58 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-58' to each side of the equation. 58 + 16x + -58 + x2 = 0 + -58 Reorder the terms: 58 + -58 + 16x + x2 = 0 + -58 Combine like terms: 58 + -58 = 0 0 + 16x + x2 = 0 + -58 16x + x2 = 0 + -58 Combine like terms: 0 + -58 = -58 16x + x2 = -58 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 = -58 + 64 Reorder the terms: 64 + 16x + x2 = -58 + 64 Combine like terms: -58 + 64 = 6 64 + 16x + x2 = 6 Factor a perfect square on the left side: (x + 8)(x + 8) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 8) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 8 = 2.449489743 Simplifying x + 8 = 2.449489743 Reorder the terms: 8 + x = 2.449489743 Solving 8 + x = 2.449489743 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 = 2.449489743 + -8 Combine like terms: 8 + -8 = 0 0 + x = 2.449489743 + -8 x = 2.449489743 + -8 Combine like terms: 2.449489743 + -8 = -5.550510257 x = -5.550510257 Simplifying x = -5.550510257Subproblem 2
x + 8 = -2.449489743 Simplifying x + 8 = -2.449489743 Reorder the terms: 8 + x = -2.449489743 Solving 8 + x = -2.449489743 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 = -2.449489743 + -8 Combine like terms: 8 + -8 = 0 0 + x = -2.449489743 + -8 x = -2.449489743 + -8 Combine like terms: -2.449489743 + -8 = -10.449489743 x = -10.449489743 Simplifying x = -10.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.550510257, -10.449489743}
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