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Simplifying x4 + -12x2 + -324 = 0 Reorder the terms: -324 + -12x2 + x4 = 0 Solving -324 + -12x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '324' to each side of the equation. -324 + -12x2 + 324 + x4 = 0 + 324 Reorder the terms: -324 + 324 + -12x2 + x4 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + -12x2 + x4 = 0 + 324 -12x2 + x4 = 0 + 324 Combine like terms: 0 + 324 = 324 -12x2 + x4 = 324 The x term is -12x2. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x2 + 36 + x4 = 324 + 36 Reorder the terms: 36 + -12x2 + x4 = 324 + 36 Combine like terms: 324 + 36 = 360 36 + -12x2 + x4 = 360 Factor a perfect square on the left side: (x2 + -6)(x2 + -6) = 360 Calculate the square root of the right side: 18.973665961 Break this problem into two subproblems by setting (x2 + -6) equal to 18.973665961 and -18.973665961.Subproblem 1
x2 + -6 = 18.973665961 Simplifying x2 + -6 = 18.973665961 Reorder the terms: -6 + x2 = 18.973665961 Solving -6 + x2 = 18.973665961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = 18.973665961 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = 18.973665961 + 6 x2 = 18.973665961 + 6 Combine like terms: 18.973665961 + 6 = 24.973665961 x2 = 24.973665961 Simplifying x2 = 24.973665961 Take the square root of each side: x = {-4.997365902, 4.997365902}Subproblem 2
x2 + -6 = -18.973665961 Simplifying x2 + -6 = -18.973665961 Reorder the terms: -6 + x2 = -18.973665961 Solving -6 + x2 = -18.973665961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x2 = -18.973665961 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = -18.973665961 + 6 x2 = -18.973665961 + 6 Combine like terms: -18.973665961 + 6 = -12.973665961 x2 = -12.973665961 Simplifying x2 = -12.973665961 Reorder the terms: 12.973665961 + x2 = -12.973665961 + 12.973665961 Combine like terms: -12.973665961 + 12.973665961 = 0.000000000 12.973665961 + 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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