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Simplifying 4 + -14x2 + -4x4 = 0 Solving 4 + -14x2 + -4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -7x2 + -2x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -7x2 + -2x4)' equal to zero and attempt to solve: Simplifying 2 + -7x2 + -2x4 = 0 Solving 2 + -7x2 + -2x4 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1 + 3.5x2 + x4 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 3.5x2 + 1 + x4 = 0 + 1 Reorder the terms: -1 + 1 + 3.5x2 + x4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3.5x2 + x4 = 0 + 1 3.5x2 + x4 = 0 + 1 Combine like terms: 0 + 1 = 1 3.5x2 + x4 = 1 The x term is 3.5x2. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x2 + 3.0625 + x4 = 1 + 3.0625 Reorder the terms: 3.0625 + 3.5x2 + x4 = 1 + 3.0625 Combine like terms: 1 + 3.0625 = 4.0625 3.0625 + 3.5x2 + x4 = 4.0625 Factor a perfect square on the left side: (x2 + 1.75)(x2 + 1.75) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x2 + 1.75) equal to 2.015564437 and -2.015564437.Subproblem 1
x2 + 1.75 = 2.015564437 Simplifying x2 + 1.75 = 2.015564437 Reorder the terms: 1.75 + x2 = 2.015564437 Solving 1.75 + x2 = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x2 = 2.015564437 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x2 = 2.015564437 + -1.75 x2 = 2.015564437 + -1.75 Combine like terms: 2.015564437 + -1.75 = 0.265564437 x2 = 0.265564437 Simplifying x2 = 0.265564437 Take the square root of each side: x = {-0.515329445, 0.515329445}Subproblem 2
x2 + 1.75 = -2.015564437 Simplifying x2 + 1.75 = -2.015564437 Reorder the terms: 1.75 + x2 = -2.015564437 Solving 1.75 + x2 = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x2 = -2.015564437 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x2 = -2.015564437 + -1.75 x2 = -2.015564437 + -1.75 Combine like terms: -2.015564437 + -1.75 = -3.765564437 x2 = -3.765564437 Simplifying x2 = -3.765564437 Reorder the terms: 3.765564437 + x2 = -3.765564437 + 3.765564437 Combine like terms: -3.765564437 + 3.765564437 = 0.000000000 3.765564437 + 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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