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Simplifying 2x4 + -13x2 + -28 = 0 Reorder the terms: -28 + -13x2 + 2x4 = 0 Solving -28 + -13x2 + 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'. -14 + -6.5x2 + x4 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -6.5x2 + 14 + x4 = 0 + 14 Reorder the terms: -14 + 14 + -6.5x2 + x4 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -6.5x2 + x4 = 0 + 14 -6.5x2 + x4 = 0 + 14 Combine like terms: 0 + 14 = 14 -6.5x2 + x4 = 14 The x term is -6.5x2. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x2 + 10.5625 + x4 = 14 + 10.5625 Reorder the terms: 10.5625 + -6.5x2 + x4 = 14 + 10.5625 Combine like terms: 14 + 10.5625 = 24.5625 10.5625 + -6.5x2 + x4 = 24.5625 Factor a perfect square on the left side: (x2 + -3.25)(x2 + -3.25) = 24.5625 Calculate the square root of the right side: 4.9560569 Break this problem into two subproblems by setting (x2 + -3.25) equal to 4.9560569 and -4.9560569.Subproblem 1
x2 + -3.25 = 4.9560569 Simplifying x2 + -3.25 = 4.9560569 Reorder the terms: -3.25 + x2 = 4.9560569 Solving -3.25 + x2 = 4.9560569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x2 = 4.9560569 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x2 = 4.9560569 + 3.25 x2 = 4.9560569 + 3.25 Combine like terms: 4.9560569 + 3.25 = 8.2060569 x2 = 8.2060569 Simplifying x2 = 8.2060569 Take the square root of each side: x = {-2.864621598, 2.864621598}Subproblem 2
x2 + -3.25 = -4.9560569 Simplifying x2 + -3.25 = -4.9560569 Reorder the terms: -3.25 + x2 = -4.9560569 Solving -3.25 + x2 = -4.9560569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x2 = -4.9560569 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x2 = -4.9560569 + 3.25 x2 = -4.9560569 + 3.25 Combine like terms: -4.9560569 + 3.25 = -1.7060569 x2 = -1.7060569 Simplifying x2 = -1.7060569 Reorder the terms: 1.7060569 + x2 = -1.7060569 + 1.7060569 Combine like terms: -1.7060569 + 1.7060569 = 0.0000000 1.7060569 + x2 = 0.0000000 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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