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Simplifying (x + -6)(x + -6) + -5 = 0 Reorder the terms: (-6 + x)(x + -6) + -5 = 0 Reorder the terms: (-6 + x)(-6 + x) + -5 = 0 Multiply (-6 + x) * (-6 + x) (-6(-6 + x) + x(-6 + x)) + -5 = 0 ((-6 * -6 + x * -6) + x(-6 + x)) + -5 = 0 ((36 + -6x) + x(-6 + x)) + -5 = 0 (36 + -6x + (-6 * x + x * x)) + -5 = 0 (36 + -6x + (-6x + x2)) + -5 = 0 Combine like terms: -6x + -6x = -12x (36 + -12x + x2) + -5 = 0 Reorder the terms: 36 + -5 + -12x + x2 = 0 Combine like terms: 36 + -5 = 31 31 + -12x + x2 = 0 Solving 31 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + -12x + -31 + x2 = 0 + -31 Reorder the terms: 31 + -31 + -12x + x2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -12x + x2 = 0 + -31 -12x + x2 = 0 + -31 Combine like terms: 0 + -31 = -31 -12x + x2 = -31 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -31 + 36 Reorder the terms: 36 + -12x + x2 = -31 + 36 Combine like terms: -31 + 36 = 5 36 + -12x + x2 = 5 Factor a perfect square on the left side: (x + -6)(x + -6) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -6) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -6 = 2.236067978 Simplifying x + -6 = 2.236067978 Reorder the terms: -6 + x = 2.236067978 Solving -6 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 2.236067978 + 6 Combine like terms: -6 + 6 = 0 0 + x = 2.236067978 + 6 x = 2.236067978 + 6 Combine like terms: 2.236067978 + 6 = 8.236067978 x = 8.236067978 Simplifying x = 8.236067978Subproblem 2
x + -6 = -2.236067978 Simplifying x + -6 = -2.236067978 Reorder the terms: -6 + x = -2.236067978 Solving -6 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -2.236067978 + 6 Combine like terms: -6 + 6 = 0 0 + x = -2.236067978 + 6 x = -2.236067978 + 6 Combine like terms: -2.236067978 + 6 = 3.763932022 x = 3.763932022 Simplifying x = 3.763932022Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.236067978, 3.763932022}
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