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Simplifying 22x2 + 2x + -2 = 0 Reorder the terms: -2 + 2x + 22x2 = 0 Solving -2 + 2x + 22x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + x + 11x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + x + 11x2)' equal to zero and attempt to solve: Simplifying -1 + x + 11x2 = 0 Solving -1 + x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.09090909091 + 0.09090909091x + x2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + 0.09090909091x + 0.09090909091 + x2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + 0.09090909091x + x2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + 0.09090909091x + x2 = 0 + 0.09090909091 0.09090909091x + x2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 0.09090909091x + x2 = 0.09090909091 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.09090909091x + 0.25 + x2 = 0.09090909091 + 0.25 Reorder the terms: 0.25 + 0.09090909091x + x2 = 0.09090909091 + 0.25 Combine like terms: 0.09090909091 + 0.25 = 0.34090909091 0.25 + 0.09090909091x + x2 = 0.34090909091 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.34090909091 Calculate the square root of the right side: 0.583874208 Break this problem into two subproblems by setting (x + 0.5) equal to 0.583874208 and -0.583874208.Subproblem 1
x + 0.5 = 0.583874208 Simplifying x + 0.5 = 0.583874208 Reorder the terms: 0.5 + x = 0.583874208 Solving 0.5 + x = 0.583874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.583874208 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.583874208 + -0.5 x = 0.583874208 + -0.5 Combine like terms: 0.583874208 + -0.5 = 0.083874208 x = 0.083874208 Simplifying x = 0.083874208Subproblem 2
x + 0.5 = -0.583874208 Simplifying x + 0.5 = -0.583874208 Reorder the terms: 0.5 + x = -0.583874208 Solving 0.5 + x = -0.583874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.583874208 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.583874208 + -0.5 x = -0.583874208 + -0.5 Combine like terms: -0.583874208 + -0.5 = -1.083874208 x = -1.083874208 Simplifying x = -1.083874208Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.083874208, -1.083874208}Solution
x = {0.083874208, -1.083874208}
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