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Simplifying 0 = 10x4 + 20x2 + -10 Reorder the terms: 0 = -10 + 20x2 + 10x4 Solving 0 = -10 + 20x2 + 10x4 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + -20x2 + -10x4 = -10 + 20x2 + 10x4 + 10 + -20x2 + -10x4 Reorder the terms: 10 + -20x2 + -10x4 = -10 + 10 + 20x2 + -20x2 + 10x4 + -10x4 Combine like terms: -10 + 10 = 0 10 + -20x2 + -10x4 = 0 + 20x2 + -20x2 + 10x4 + -10x4 10 + -20x2 + -10x4 = 20x2 + -20x2 + 10x4 + -10x4 Combine like terms: 20x2 + -20x2 = 0 10 + -20x2 + -10x4 = 0 + 10x4 + -10x4 10 + -20x2 + -10x4 = 10x4 + -10x4 Combine like terms: 10x4 + -10x4 = 0 10 + -20x2 + -10x4 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(1 + -2x2 + -1x4) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(1 + -2x2 + -1x4)' equal to zero and attempt to solve: Simplifying 1 + -2x2 + -1x4 = 0 Solving 1 + -2x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + 2x2 + x4 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 2x2 + 1 + x4 = 0 + 1 Reorder the terms: -1 + 1 + 2x2 + x4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x2 + x4 = 0 + 1 2x2 + x4 = 0 + 1 Combine like terms: 0 + 1 = 1 2x2 + x4 = 1 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = 1 + 1 Reorder the terms: 1 + 2x2 + x4 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + 2x2 + x4 = 2 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x2 + 1) equal to 1.414213562 and -1.414213562.Subproblem 1
x2 + 1 = 1.414213562 Simplifying x2 + 1 = 1.414213562 Reorder the terms: 1 + x2 = 1.414213562 Solving 1 + x2 = 1.414213562 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 + x2 = 1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 1.414213562 + -1 x2 = 1.414213562 + -1 Combine like terms: 1.414213562 + -1 = 0.414213562 x2 = 0.414213562 Simplifying x2 = 0.414213562 Take the square root of each side: x = {-0.643594253, 0.643594253}Subproblem 2
x2 + 1 = -1.414213562 Simplifying x2 + 1 = -1.414213562 Reorder the terms: 1 + x2 = -1.414213562 Solving 1 + x2 = -1.414213562 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 + x2 = -1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -1.414213562 + -1 x2 = -1.414213562 + -1 Combine like terms: -1.414213562 + -1 = -2.414213562 x2 = -2.414213562 Simplifying x2 = -2.414213562 Reorder the terms: 2.414213562 + x2 = -2.414213562 + 2.414213562 Combine like terms: -2.414213562 + 2.414213562 = 0.000000000 2.414213562 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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