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Simplifying 6x4 + -24x2 + -54 = 0 Reorder the terms: -54 + -24x2 + 6x4 = 0 Solving -54 + -24x2 + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-9 + -4x2 + x4) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-9 + -4x2 + x4)' equal to zero and attempt to solve: Simplifying -9 + -4x2 + x4 = 0 Solving -9 + -4x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -4x2 + 9 + x4 = 0 + 9 Reorder the terms: -9 + 9 + -4x2 + x4 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4x2 + x4 = 0 + 9 -4x2 + x4 = 0 + 9 Combine like terms: 0 + 9 = 9 -4x2 + x4 = 9 The x term is -4x2. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x2 + 4 + x4 = 9 + 4 Reorder the terms: 4 + -4x2 + x4 = 9 + 4 Combine like terms: 9 + 4 = 13 4 + -4x2 + x4 = 13 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x2 + -2) equal to 3.605551275 and -3.605551275.Subproblem 1
x2 + -2 = 3.605551275 Simplifying x2 + -2 = 3.605551275 Reorder the terms: -2 + x2 = 3.605551275 Solving -2 + x2 = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = 3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 3.605551275 + 2 x2 = 3.605551275 + 2 Combine like terms: 3.605551275 + 2 = 5.605551275 x2 = 5.605551275 Simplifying x2 = 5.605551275 Take the square root of each side: x = {-2.367604544, 2.367604544}Subproblem 2
x2 + -2 = -3.605551275 Simplifying x2 + -2 = -3.605551275 Reorder the terms: -2 + x2 = -3.605551275 Solving -2 + x2 = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = -3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -3.605551275 + 2 x2 = -3.605551275 + 2 Combine like terms: -3.605551275 + 2 = -1.605551275 x2 = -1.605551275 Simplifying x2 = -1.605551275 Reorder the terms: 1.605551275 + x2 = -1.605551275 + 1.605551275 Combine like terms: -1.605551275 + 1.605551275 = 0.000000000 1.605551275 + 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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