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Simplifying ((x + 16)(x + 16)) + -5 = 0 Reorder the terms: ((16 + x)(x + 16)) + -5 = 0 Reorder the terms: ((16 + x)(16 + x)) + -5 = 0 Multiply (16 + x) * (16 + x) ((16(16 + x) + x(16 + x))) + -5 = 0 (((16 * 16 + x * 16) + x(16 + x))) + -5 = 0 (((256 + 16x) + x(16 + x))) + -5 = 0 ((256 + 16x + (16 * x + x * x))) + -5 = 0 ((256 + 16x + (16x + x2))) + -5 = 0 Combine like terms: 16x + 16x = 32x ((256 + 32x + x2)) + -5 = 0 (256 + 32x + x2) + -5 = 0 Remove parenthesis around (256 + 32x + x2) 256 + 32x + x2 + -5 = 0 Reorder the terms: 256 + -5 + 32x + x2 = 0 Combine like terms: 256 + -5 = 251 251 + 32x + x2 = 0 Solving 251 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-251' to each side of the equation. 251 + 32x + -251 + x2 = 0 + -251 Reorder the terms: 251 + -251 + 32x + x2 = 0 + -251 Combine like terms: 251 + -251 = 0 0 + 32x + x2 = 0 + -251 32x + x2 = 0 + -251 Combine like terms: 0 + -251 = -251 32x + x2 = -251 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 = -251 + 256 Reorder the terms: 256 + 32x + x2 = -251 + 256 Combine like terms: -251 + 256 = 5 256 + 32x + x2 = 5 Factor a perfect square on the left side: (x + 16)(x + 16) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + 16) equal to 2.236067978 and -2.236067978.Subproblem 1
x + 16 = 2.236067978 Simplifying x + 16 = 2.236067978 Reorder the terms: 16 + x = 2.236067978 Solving 16 + x = 2.236067978 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 = 2.236067978 + -16 Combine like terms: 16 + -16 = 0 0 + x = 2.236067978 + -16 x = 2.236067978 + -16 Combine like terms: 2.236067978 + -16 = -13.763932022 x = -13.763932022 Simplifying x = -13.763932022Subproblem 2
x + 16 = -2.236067978 Simplifying x + 16 = -2.236067978 Reorder the terms: 16 + x = -2.236067978 Solving 16 + x = -2.236067978 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 = -2.236067978 + -16 Combine like terms: 16 + -16 = 0 0 + x = -2.236067978 + -16 x = -2.236067978 + -16 Combine like terms: -2.236067978 + -16 = -18.236067978 x = -18.236067978 Simplifying x = -18.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {-13.763932022, -18.236067978}
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