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Simplifying (x + 16)(x + 16) + -2 = 0 Reorder the terms: (16 + x)(x + 16) + -2 = 0 Reorder the terms: (16 + x)(16 + x) + -2 = 0 Multiply (16 + x) * (16 + x) (16(16 + x) + x(16 + x)) + -2 = 0 ((16 * 16 + x * 16) + x(16 + x)) + -2 = 0 ((256 + 16x) + x(16 + x)) + -2 = 0 (256 + 16x + (16 * x + x * x)) + -2 = 0 (256 + 16x + (16x + x2)) + -2 = 0 Combine like terms: 16x + 16x = 32x (256 + 32x + x2) + -2 = 0 Reorder the terms: 256 + -2 + 32x + x2 = 0 Combine like terms: 256 + -2 = 254 254 + 32x + x2 = 0 Solving 254 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-254' to each side of the equation. 254 + 32x + -254 + x2 = 0 + -254 Reorder the terms: 254 + -254 + 32x + x2 = 0 + -254 Combine like terms: 254 + -254 = 0 0 + 32x + x2 = 0 + -254 32x + x2 = 0 + -254 Combine like terms: 0 + -254 = -254 32x + x2 = -254 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = -254 + 256 Reorder the terms: 256 + 32x + x2 = -254 + 256 Combine like terms: -254 + 256 = 2 256 + 32x + x2 = 2 Factor a perfect square on the left side: (x + 16)(x + 16) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 16) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 16 = 1.414213562 Simplifying x + 16 = 1.414213562 Reorder the terms: 16 + x = 1.414213562 Solving 16 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 1.414213562 + -16 Combine like terms: 16 + -16 = 0 0 + x = 1.414213562 + -16 x = 1.414213562 + -16 Combine like terms: 1.414213562 + -16 = -14.585786438 x = -14.585786438 Simplifying x = -14.585786438Subproblem 2
x + 16 = -1.414213562 Simplifying x + 16 = -1.414213562 Reorder the terms: 16 + x = -1.414213562 Solving 16 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -1.414213562 + -16 Combine like terms: 16 + -16 = 0 0 + x = -1.414213562 + -16 x = -1.414213562 + -16 Combine like terms: -1.414213562 + -16 = -17.414213562 x = -17.414213562 Simplifying x = -17.414213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-14.585786438, -17.414213562}
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