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Simplifying 2x + 10 + -9x = -1(x + 8)(x + -2) + (x + -2) Reorder the terms: 10 + 2x + -9x = -1(x + 8)(x + -2) + (x + -2) Combine like terms: 2x + -9x = -7x 10 + -7x = -1(x + 8)(x + -2) + (x + -2) Reorder the terms: 10 + -7x = -1(8 + x)(x + -2) + (x + -2) Reorder the terms: 10 + -7x = -1(8 + x)(-2 + x) + (x + -2) Multiply (8 + x) * (-2 + x) 10 + -7x = -1(8(-2 + x) + x(-2 + x)) + (x + -2) 10 + -7x = -1((-2 * 8 + x * 8) + x(-2 + x)) + (x + -2) 10 + -7x = -1((-16 + 8x) + x(-2 + x)) + (x + -2) 10 + -7x = -1(-16 + 8x + (-2 * x + x * x)) + (x + -2) 10 + -7x = -1(-16 + 8x + (-2x + x2)) + (x + -2) Combine like terms: 8x + -2x = 6x 10 + -7x = -1(-16 + 6x + x2) + (x + -2) 10 + -7x = (-16 * -1 + 6x * -1 + x2 * -1) + (x + -2) 10 + -7x = (16 + -6x + -1x2) + (x + -2) Reorder the terms: 10 + -7x = 16 + -6x + -1x2 + (-2 + x) Remove parenthesis around (-2 + x) 10 + -7x = 16 + -6x + -1x2 + -2 + x Reorder the terms: 10 + -7x = 16 + -2 + -6x + x + -1x2 Combine like terms: 16 + -2 = 14 10 + -7x = 14 + -6x + x + -1x2 Combine like terms: -6x + x = -5x 10 + -7x = 14 + -5x + -1x2 Solving 10 + -7x = 14 + -5x + -1x2 Solving for variable 'x'. Reorder the terms: 10 + -14 + -7x + 5x + x2 = 14 + -5x + -1x2 + -14 + 5x + x2 Combine like terms: 10 + -14 = -4 -4 + -7x + 5x + x2 = 14 + -5x + -1x2 + -14 + 5x + x2 Combine like terms: -7x + 5x = -2x -4 + -2x + x2 = 14 + -5x + -1x2 + -14 + 5x + x2 Reorder the terms: -4 + -2x + x2 = 14 + -14 + -5x + 5x + -1x2 + x2 Combine like terms: 14 + -14 = 0 -4 + -2x + x2 = 0 + -5x + 5x + -1x2 + x2 -4 + -2x + x2 = -5x + 5x + -1x2 + x2 Combine like terms: -5x + 5x = 0 -4 + -2x + x2 = 0 + -1x2 + x2 -4 + -2x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -4 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -2x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -2x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2x + x2 = 0 + 4 -2x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2x + x2 = 4 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 4 + 1 Reorder the terms: 1 + -2x + x2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + -2x + x2 = 5 Factor a perfect square on the left side: (x + -1)(x + -1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -1) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -1 = 2.236067978 Simplifying x + -1 = 2.236067978 Reorder the terms: -1 + x = 2.236067978 Solving -1 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.236067978 + 1 x = 2.236067978 + 1 Combine like terms: 2.236067978 + 1 = 3.236067978 x = 3.236067978 Simplifying x = 3.236067978Subproblem 2
x + -1 = -2.236067978 Simplifying x + -1 = -2.236067978 Reorder the terms: -1 + x = -2.236067978 Solving -1 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.236067978 + 1 x = -2.236067978 + 1 Combine like terms: -2.236067978 + 1 = -1.236067978 x = -1.236067978 Simplifying x = -1.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.236067978, -1.236067978}
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