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Simplifying 3x4 + -18x2 + -18 = 0 Reorder the terms: -18 + -18x2 + 3x4 = 0 Solving -18 + -18x2 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + -6x2 + x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + -6x2 + x4)' equal to zero and attempt to solve: Simplifying -6 + -6x2 + x4 = 0 Solving -6 + -6x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -6x2 + 6 + x4 = 0 + 6 Reorder the terms: -6 + 6 + -6x2 + x4 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -6x2 + x4 = 0 + 6 -6x2 + x4 = 0 + 6 Combine like terms: 0 + 6 = 6 -6x2 + x4 = 6 The x term is -6x2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x2 + 9 + x4 = 6 + 9 Reorder the terms: 9 + -6x2 + x4 = 6 + 9 Combine like terms: 6 + 9 = 15 9 + -6x2 + x4 = 15 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x2 + -3) equal to 3.872983346 and -3.872983346.Subproblem 1
x2 + -3 = 3.872983346 Simplifying x2 + -3 = 3.872983346 Reorder the terms: -3 + x2 = 3.872983346 Solving -3 + x2 = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = 3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 3.872983346 + 3 x2 = 3.872983346 + 3 Combine like terms: 3.872983346 + 3 = 6.872983346 x2 = 6.872983346 Simplifying x2 = 6.872983346 Take the square root of each side: x = {-2.621637531, 2.621637531}Subproblem 2
x2 + -3 = -3.872983346 Simplifying x2 + -3 = -3.872983346 Reorder the terms: -3 + x2 = -3.872983346 Solving -3 + x2 = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = -3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -3.872983346 + 3 x2 = -3.872983346 + 3 Combine like terms: -3.872983346 + 3 = -0.872983346 x2 = -0.872983346 Simplifying x2 = -0.872983346 Reorder the terms: 0.872983346 + x2 = -0.872983346 + 0.872983346 Combine like terms: -0.872983346 + 0.872983346 = 0.000000000 0.872983346 + 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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