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Simplifying 2x + [2x + -1(x + -4)] = [-1x(-5 + -1x)] Reorder the terms: 2x + [2x + -1(-4 + x)] = [-1x(-5 + -1x)] 2x + [2x + (-4 * -1 + x * -1)] = [-1x(-5 + -1x)] 2x + [2x + (4 + -1x)] = [-1x(-5 + -1x)] Reorder the terms: 2x + [4 + 2x + -1x] = [-1x(-5 + -1x)] Combine like terms: 2x + -1x = 1x 2x + [4 + 1x] = [-1x(-5 + -1x)] Remove brackets around [4 + 1x] 2x + 4 + 1x = [-1x(-5 + -1x)] Reorder the terms: 4 + 2x + 1x = [-1x(-5 + -1x)] Combine like terms: 2x + 1x = 3x 4 + 3x = [-1x(-5 + -1x)] 4 + 3x = [(-5 * -1x + -1x * -1x)] 4 + 3x = [(5x + 1x2)] 4 + 3x = [5x + 1x2] Remove brackets around [5x + 1x2] 4 + 3x = 5x + 1x2 Solving 4 + 3x = 5x + 1x2 Solving for variable 'x'. Combine like terms: 3x + -5x = -2x 4 + -2x + -1x2 = 5x + 1x2 + -5x + -1x2 Reorder the terms: 4 + -2x + -1x2 = 5x + -5x + 1x2 + -1x2 Combine like terms: 5x + -5x = 0 4 + -2x + -1x2 = 0 + 1x2 + -1x2 4 + -2x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 4 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 2x + x2 = 0 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 = 1.236067978 x = 1.236067978 Simplifying x = 1.236067978Subproblem 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 = -3.236067978 x = -3.236067978 Simplifying x = -3.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.236067978, -3.236067978}
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