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Simplifying x2 + -16x + 59 = 0 Reorder the terms: 59 + -16x + x2 = 0 Solving 59 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-59' to each side of the equation. 59 + -16x + -59 + x2 = 0 + -59 Reorder the terms: 59 + -59 + -16x + x2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + -16x + x2 = 0 + -59 -16x + x2 = 0 + -59 Combine like terms: 0 + -59 = -59 -16x + x2 = -59 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 = -59 + 64 Reorder the terms: 64 + -16x + x2 = -59 + 64 Combine like terms: -59 + 64 = 5 64 + -16x + x2 = 5 Factor a perfect square on the left side: (x + -8)(x + -8) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -8) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -8 = 2.236067978 Simplifying x + -8 = 2.236067978 Reorder the terms: -8 + x = 2.236067978 Solving -8 + x = 2.236067978 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 = 2.236067978 + 8 Combine like terms: -8 + 8 = 0 0 + x = 2.236067978 + 8 x = 2.236067978 + 8 Combine like terms: 2.236067978 + 8 = 10.236067978 x = 10.236067978 Simplifying x = 10.236067978Subproblem 2
x + -8 = -2.236067978 Simplifying x + -8 = -2.236067978 Reorder the terms: -8 + x = -2.236067978 Solving -8 + x = -2.236067978 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 = -2.236067978 + 8 Combine like terms: -8 + 8 = 0 0 + x = -2.236067978 + 8 x = -2.236067978 + 8 Combine like terms: -2.236067978 + 8 = 5.763932022 x = 5.763932022 Simplifying x = 5.763932022Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.236067978, 5.763932022}
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