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Simplifying (x + 2)(x + 8) = -4 Reorder the terms: (2 + x)(x + 8) = -4 Reorder the terms: (2 + x)(8 + x) = -4 Multiply (2 + x) * (8 + x) (2(8 + x) + x(8 + x)) = -4 ((8 * 2 + x * 2) + x(8 + x)) = -4 ((16 + 2x) + x(8 + x)) = -4 (16 + 2x + (8 * x + x * x)) = -4 (16 + 2x + (8x + x2)) = -4 Combine like terms: 2x + 8x = 10x (16 + 10x + x2) = -4 Solving 16 + 10x + x2 = -4 Solving for variable 'x'. Reorder the terms: 16 + 4 + 10x + x2 = -4 + 4 Combine like terms: 16 + 4 = 20 20 + 10x + x2 = -4 + 4 Combine like terms: -4 + 4 = 0 20 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 10x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 10x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 10x + x2 = 0 + -20 10x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 10x + x2 = -20 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -20 + 25 Reorder the terms: 25 + 10x + x2 = -20 + 25 Combine like terms: -20 + 25 = 5 25 + 10x + x2 = 5 Factor a perfect square on the left side: (x + 5)(x + 5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + 5) equal to 2.236067978 and -2.236067978.Subproblem 1
x + 5 = 2.236067978 Simplifying x + 5 = 2.236067978 Reorder the terms: 5 + x = 2.236067978 Solving 5 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 2.236067978 + -5 Combine like terms: 5 + -5 = 0 0 + x = 2.236067978 + -5 x = 2.236067978 + -5 Combine like terms: 2.236067978 + -5 = -2.763932022 x = -2.763932022 Simplifying x = -2.763932022Subproblem 2
x + 5 = -2.236067978 Simplifying x + 5 = -2.236067978 Reorder the terms: 5 + x = -2.236067978 Solving 5 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -2.236067978 + -5 Combine like terms: 5 + -5 = 0 0 + x = -2.236067978 + -5 x = -2.236067978 + -5 Combine like terms: -2.236067978 + -5 = -7.236067978 x = -7.236067978 Simplifying x = -7.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.763932022, -7.236067978}
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