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Simplifying x2 = 2(x + -1)(x + -2) Reorder the terms: x2 = 2(-1 + x)(x + -2) Reorder the terms: x2 = 2(-1 + x)(-2 + x) Multiply (-1 + x) * (-2 + x) x2 = 2(-1(-2 + x) + x(-2 + x)) x2 = 2((-2 * -1 + x * -1) + x(-2 + x)) x2 = 2((2 + -1x) + x(-2 + x)) x2 = 2(2 + -1x + (-2 * x + x * x)) x2 = 2(2 + -1x + (-2x + x2)) Combine like terms: -1x + -2x = -3x x2 = 2(2 + -3x + x2) x2 = (2 * 2 + -3x * 2 + x2 * 2) x2 = (4 + -6x + 2x2) Solving x2 = 4 + -6x + 2x2 Solving for variable 'x'. Reorder the terms: -4 + 6x + x2 + -2x2 = 4 + -6x + 2x2 + -4 + 6x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -4 + 6x + -1x2 = 4 + -6x + 2x2 + -4 + 6x + -2x2 Reorder the terms: -4 + 6x + -1x2 = 4 + -4 + -6x + 6x + 2x2 + -2x2 Combine like terms: 4 + -4 = 0 -4 + 6x + -1x2 = 0 + -6x + 6x + 2x2 + -2x2 -4 + 6x + -1x2 = -6x + 6x + 2x2 + -2x2 Combine like terms: -6x + 6x = 0 -4 + 6x + -1x2 = 0 + 2x2 + -2x2 -4 + 6x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -4 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -6x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -6x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6x + x2 = 0 + -4 -6x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -6x + x2 = -4 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -4 + 9 Reorder the terms: 9 + -6x + x2 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + -6x + x2 = 5 Factor a perfect square on the left side: (x + -3)(x + -3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -3) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -3 = 2.236067978 Simplifying x + -3 = 2.236067978 Reorder the terms: -3 + x = 2.236067978 Solving -3 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.236067978 + 3 x = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 x = 5.236067978 Simplifying x = 5.236067978Subproblem 2
x + -3 = -2.236067978 Simplifying x + -3 = -2.236067978 Reorder the terms: -3 + x = -2.236067978 Solving -3 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.236067978 + 3 x = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 x = 0.763932022 Simplifying x = 0.763932022Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.236067978, 0.763932022}
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