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Simplifying x + -2 = (x + -2)(x + -2) + -1 Reorder the terms: -2 + x = (x + -2)(x + -2) + -1 Reorder the terms: -2 + x = (-2 + x)(x + -2) + -1 Reorder the terms: -2 + x = (-2 + x)(-2 + x) + -1 Multiply (-2 + x) * (-2 + x) -2 + x = (-2(-2 + x) + x(-2 + x)) + -1 -2 + x = ((-2 * -2 + x * -2) + x(-2 + x)) + -1 -2 + x = ((4 + -2x) + x(-2 + x)) + -1 -2 + x = (4 + -2x + (-2 * x + x * x)) + -1 -2 + x = (4 + -2x + (-2x + x2)) + -1 Combine like terms: -2x + -2x = -4x -2 + x = (4 + -4x + x2) + -1 Reorder the terms: -2 + x = 4 + -1 + -4x + x2 Combine like terms: 4 + -1 = 3 -2 + x = 3 + -4x + x2 Solving -2 + x = 3 + -4x + x2 Solving for variable 'x'. Reorder the terms: -2 + -3 + x + 4x + -1x2 = 3 + -4x + x2 + -3 + 4x + -1x2 Combine like terms: -2 + -3 = -5 -5 + x + 4x + -1x2 = 3 + -4x + x2 + -3 + 4x + -1x2 Combine like terms: x + 4x = 5x -5 + 5x + -1x2 = 3 + -4x + x2 + -3 + 4x + -1x2 Reorder the terms: -5 + 5x + -1x2 = 3 + -3 + -4x + 4x + x2 + -1x2 Combine like terms: 3 + -3 = 0 -5 + 5x + -1x2 = 0 + -4x + 4x + x2 + -1x2 -5 + 5x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 -5 + 5x + -1x2 = 0 + x2 + -1x2 -5 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -5 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -5x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -5x + x2 = 0 + -5 -5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -5x + x2 = -5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -5 + 6.25 Combine like terms: -5 + 6.25 = 1.25 6.25 + -5x + x2 = 1.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -2.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -2.5 = 1.118033989 Simplifying x + -2.5 = 1.118033989 Reorder the terms: -2.5 + x = 1.118033989 Solving -2.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.118033989 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.118033989 + 2.5 x = 1.118033989 + 2.5 Combine like terms: 1.118033989 + 2.5 = 3.618033989 x = 3.618033989 Simplifying x = 3.618033989Subproblem 2
x + -2.5 = -1.118033989 Simplifying x + -2.5 = -1.118033989 Reorder the terms: -2.5 + x = -1.118033989 Solving -2.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.118033989 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.118033989 + 2.5 x = -1.118033989 + 2.5 Combine like terms: -1.118033989 + 2.5 = 1.381966011 x = 1.381966011 Simplifying x = 1.381966011Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.618033989, 1.381966011}
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