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Simplifying x + -2(x2 + -4x + 4) + x + -2 = 0 Reorder the terms: x + -2(4 + -4x + x2) + x + -2 = 0 x + (4 * -2 + -4x * -2 + x2 * -2) + x + -2 = 0 x + (-8 + 8x + -2x2) + x + -2 = 0 Reorder the terms: -8 + -2 + x + 8x + x + -2x2 = 0 Combine like terms: -8 + -2 = -10 -10 + x + 8x + x + -2x2 = 0 Combine like terms: x + 8x = 9x -10 + 9x + x + -2x2 = 0 Combine like terms: 9x + x = 10x -10 + 10x + -2x2 = 0 Solving -10 + 10x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 5x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 5x + -1x2)' equal to zero and attempt to solve: Simplifying -5 + 5x + -1x2 = 0 Solving -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}Solution
x = {3.618033989, 1.381966011}
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