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Simplifying 2x4 + 14x2 + -3 = 0 Reorder the terms: -3 + 14x2 + 2x4 = 0 Solving -3 + 14x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 7x2 + x4 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 7x2 + 1.5 + x4 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 7x2 + x4 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 7x2 + x4 = 0 + 1.5 7x2 + x4 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 7x2 + x4 = 1.5 The x term is 7x2. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x2 + 12.25 + x4 = 1.5 + 12.25 Reorder the terms: 12.25 + 7x2 + x4 = 1.5 + 12.25 Combine like terms: 1.5 + 12.25 = 13.75 12.25 + 7x2 + x4 = 13.75 Factor a perfect square on the left side: (x2 + 3.5)(x2 + 3.5) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (x2 + 3.5) equal to 3.708099244 and -3.708099244.Subproblem 1
x2 + 3.5 = 3.708099244 Simplifying x2 + 3.5 = 3.708099244 Reorder the terms: 3.5 + x2 = 3.708099244 Solving 3.5 + x2 = 3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x2 = 3.708099244 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x2 = 3.708099244 + -3.5 x2 = 3.708099244 + -3.5 Combine like terms: 3.708099244 + -3.5 = 0.208099244 x2 = 0.208099244 Simplifying x2 = 0.208099244 Take the square root of each side: x = {-0.45617896, 0.45617896}Subproblem 2
x2 + 3.5 = -3.708099244 Simplifying x2 + 3.5 = -3.708099244 Reorder the terms: 3.5 + x2 = -3.708099244 Solving 3.5 + x2 = -3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x2 = -3.708099244 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x2 = -3.708099244 + -3.5 x2 = -3.708099244 + -3.5 Combine like terms: -3.708099244 + -3.5 = -7.208099244 x2 = -7.208099244 Simplifying x2 = -7.208099244 Reorder the terms: 7.208099244 + x2 = -7.208099244 + 7.208099244 Combine like terms: -7.208099244 + 7.208099244 = 0.000000000 7.208099244 + 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.
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