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Simplifying -1x2 + -16x + -59 = 0 Reorder the terms: -59 + -16x + -1x2 = 0 Solving -59 + -16x + -1x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(59 + 16x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(59 + 16x + x2)' equal to zero and attempt to solve: Simplifying 59 + 16x + x2 = 0 Solving 59 + 16x + x2 = 0 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 = -5.763932022 x = -5.763932022 Simplifying x = -5.763932022Subproblem 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 = -10.236067978 x = -10.236067978 Simplifying x = -10.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.763932022, -10.236067978}Solution
x = {-5.763932022, -10.236067978}
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