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Simplifying (x + 8)(x + 8) = 2 Reorder the terms: (8 + x)(x + 8) = 2 Reorder the terms: (8 + x)(8 + x) = 2 Multiply (8 + x) * (8 + x) (8(8 + x) + x(8 + x)) = 2 ((8 * 8 + x * 8) + x(8 + x)) = 2 ((64 + 8x) + x(8 + x)) = 2 (64 + 8x + (8 * x + x * x)) = 2 (64 + 8x + (8x + x2)) = 2 Combine like terms: 8x + 8x = 16x (64 + 16x + x2) = 2 Solving 64 + 16x + x2 = 2 Solving for variable 'x'. Reorder the terms: 64 + -2 + 16x + x2 = 2 + -2 Combine like terms: 64 + -2 = 62 62 + 16x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 62 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-62' to each side of the equation. 62 + 16x + -62 + x2 = 0 + -62 Reorder the terms: 62 + -62 + 16x + x2 = 0 + -62 Combine like terms: 62 + -62 = 0 0 + 16x + x2 = 0 + -62 16x + x2 = 0 + -62 Combine like terms: 0 + -62 = -62 16x + x2 = -62 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 = -62 + 64 Reorder the terms: 64 + 16x + x2 = -62 + 64 Combine like terms: -62 + 64 = 2 64 + 16x + x2 = 2 Factor a perfect square on the left side: (x + 8)(x + 8) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 8) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 8 = 1.414213562 Simplifying x + 8 = 1.414213562 Reorder the terms: 8 + x = 1.414213562 Solving 8 + x = 1.414213562 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 = 1.414213562 + -8 Combine like terms: 8 + -8 = 0 0 + x = 1.414213562 + -8 x = 1.414213562 + -8 Combine like terms: 1.414213562 + -8 = -6.585786438 x = -6.585786438 Simplifying x = -6.585786438Subproblem 2
x + 8 = -1.414213562 Simplifying x + 8 = -1.414213562 Reorder the terms: 8 + x = -1.414213562 Solving 8 + x = -1.414213562 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 = -1.414213562 + -8 Combine like terms: 8 + -8 = 0 0 + x = -1.414213562 + -8 x = -1.414213562 + -8 Combine like terms: -1.414213562 + -8 = -9.414213562 x = -9.414213562 Simplifying x = -9.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.585786438, -9.414213562}
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