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Simplifying x + x = 2(x + -2)(x + 1) Combine like terms: x + x = 2x 2x = 2(x + -2)(x + 1) Reorder the terms: 2x = 2(-2 + x)(x + 1) Reorder the terms: 2x = 2(-2 + x)(1 + x) Multiply (-2 + x) * (1 + x) 2x = 2(-2(1 + x) + x(1 + x)) 2x = 2((1 * -2 + x * -2) + x(1 + x)) 2x = 2((-2 + -2x) + x(1 + x)) 2x = 2(-2 + -2x + (1 * x + x * x)) 2x = 2(-2 + -2x + (1x + x2)) Combine like terms: -2x + 1x = -1x 2x = 2(-2 + -1x + x2) 2x = (-2 * 2 + -1x * 2 + x2 * 2) 2x = (-4 + -2x + 2x2) Solving 2x = -4 + -2x + 2x2 Solving for variable 'x'. Reorder the terms: 4 + 2x + 2x + -2x2 = -4 + -2x + 2x2 + 4 + 2x + -2x2 Combine like terms: 2x + 2x = 4x 4 + 4x + -2x2 = -4 + -2x + 2x2 + 4 + 2x + -2x2 Reorder the terms: 4 + 4x + -2x2 = -4 + 4 + -2x + 2x + 2x2 + -2x2 Combine like terms: -4 + 4 = 0 4 + 4x + -2x2 = 0 + -2x + 2x + 2x2 + -2x2 4 + 4x + -2x2 = -2x + 2x + 2x2 + -2x2 Combine like terms: -2x + 2x = 0 4 + 4x + -2x2 = 0 + 2x2 + -2x2 4 + 4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 4 + 4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 2x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 2 + 2x + -1x2 = 0 Solving 2 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -2x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -2x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2x + x2 = 0 + 2 -2x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2x + x2 = 2 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 = 2 + 1 Reorder the terms: 1 + -2x + x2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2x + x2 = 3 Factor a perfect square on the left side: (x + -1)(x + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -1) equal to 1.732050808 and -1.732050808.Subproblem 1
x + -1 = 1.732050808 Simplifying x + -1 = 1.732050808 Reorder the terms: -1 + x = 1.732050808 Solving -1 + x = 1.732050808 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 = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.732050808 + 1 x = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 x = 2.732050808 Simplifying x = 2.732050808Subproblem 2
x + -1 = -1.732050808 Simplifying x + -1 = -1.732050808 Reorder the terms: -1 + x = -1.732050808 Solving -1 + x = -1.732050808 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 = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.732050808 + 1 x = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 x = -0.732050808 Simplifying x = -0.732050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.732050808, -0.732050808}Solution
x = {2.732050808, -0.732050808}
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