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Simplifying (x + 1)(x + -8) + 28 = 3x Reorder the terms: (1 + x)(x + -8) + 28 = 3x Reorder the terms: (1 + x)(-8 + x) + 28 = 3x Multiply (1 + x) * (-8 + x) (1(-8 + x) + x(-8 + x)) + 28 = 3x ((-8 * 1 + x * 1) + x(-8 + x)) + 28 = 3x ((-8 + 1x) + x(-8 + x)) + 28 = 3x (-8 + 1x + (-8 * x + x * x)) + 28 = 3x (-8 + 1x + (-8x + x2)) + 28 = 3x Combine like terms: 1x + -8x = -7x (-8 + -7x + x2) + 28 = 3x Reorder the terms: -8 + 28 + -7x + x2 = 3x Combine like terms: -8 + 28 = 20 20 + -7x + x2 = 3x Solving 20 + -7x + x2 = 3x Solving for variable 'x'. Reorder the terms: 20 + -7x + -3x + x2 = 3x + -3x Combine like terms: -7x + -3x = -10x 20 + -10x + x2 = 3x + -3x Combine like terms: 3x + -3x = 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 = 7.236067978 x = 7.236067978 Simplifying x = 7.236067978Subproblem 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 = 2.763932022 x = 2.763932022 Simplifying x = 2.763932022Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.236067978, 2.763932022}
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