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Simplifying 2x4 + -6x2 + -135 = 0 Reorder the terms: -135 + -6x2 + 2x4 = 0 Solving -135 + -6x2 + 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'. -67.5 + -3x2 + x4 = 0 Move the constant term to the right: Add '67.5' to each side of the equation. -67.5 + -3x2 + 67.5 + x4 = 0 + 67.5 Reorder the terms: -67.5 + 67.5 + -3x2 + x4 = 0 + 67.5 Combine like terms: -67.5 + 67.5 = 0.0 0.0 + -3x2 + x4 = 0 + 67.5 -3x2 + x4 = 0 + 67.5 Combine like terms: 0 + 67.5 = 67.5 -3x2 + x4 = 67.5 The x term is -3x2. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x2 + 2.25 + x4 = 67.5 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = 67.5 + 2.25 Combine like terms: 67.5 + 2.25 = 69.75 2.25 + -3x2 + x4 = 69.75 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = 69.75 Calculate the square root of the right side: 8.351646544 Break this problem into two subproblems by setting (x2 + -1.5) equal to 8.351646544 and -8.351646544.Subproblem 1
x2 + -1.5 = 8.351646544 Simplifying x2 + -1.5 = 8.351646544 Reorder the terms: -1.5 + x2 = 8.351646544 Solving -1.5 + x2 = 8.351646544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = 8.351646544 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 8.351646544 + 1.5 x2 = 8.351646544 + 1.5 Combine like terms: 8.351646544 + 1.5 = 9.851646544 x2 = 9.851646544 Simplifying x2 = 9.851646544 Take the square root of each side: x = {-3.138733271, 3.138733271}Subproblem 2
x2 + -1.5 = -8.351646544 Simplifying x2 + -1.5 = -8.351646544 Reorder the terms: -1.5 + x2 = -8.351646544 Solving -1.5 + x2 = -8.351646544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = -8.351646544 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -8.351646544 + 1.5 x2 = -8.351646544 + 1.5 Combine like terms: -8.351646544 + 1.5 = -6.851646544 x2 = -6.851646544 Simplifying x2 = -6.851646544 Reorder the terms: 6.851646544 + x2 = -6.851646544 + 6.851646544 Combine like terms: -6.851646544 + 6.851646544 = 0.000000000 6.851646544 + 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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