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Simplifying 6x4 + -56x2 + -162 = 0 Reorder the terms: -162 + -56x2 + 6x4 = 0 Solving -162 + -56x2 + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-81 + -28x2 + 3x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-81 + -28x2 + 3x4)' equal to zero and attempt to solve: Simplifying -81 + -28x2 + 3x4 = 0 Solving -81 + -28x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -27 + -9.333333333x2 + x4 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -9.333333333x2 + 27 + x4 = 0 + 27 Reorder the terms: -27 + 27 + -9.333333333x2 + x4 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -9.333333333x2 + x4 = 0 + 27 -9.333333333x2 + x4 = 0 + 27 Combine like terms: 0 + 27 = 27 -9.333333333x2 + x4 = 27 The x term is -9.333333333x2. Take half its coefficient (-4.666666667). Square it (21.77777778) and add it to both sides. Add '21.77777778' to each side of the equation. -9.333333333x2 + 21.77777778 + x4 = 27 + 21.77777778 Reorder the terms: 21.77777778 + -9.333333333x2 + x4 = 27 + 21.77777778 Combine like terms: 27 + 21.77777778 = 48.77777778 21.77777778 + -9.333333333x2 + x4 = 48.77777778 Factor a perfect square on the left side: (x2 + -4.666666667)(x2 + -4.666666667) = 48.77777778 Calculate the square root of the right side: 6.984108947 Break this problem into two subproblems by setting (x2 + -4.666666667) equal to 6.984108947 and -6.984108947.Subproblem 1
x2 + -4.666666667 = 6.984108947 Simplifying x2 + -4.666666667 = 6.984108947 Reorder the terms: -4.666666667 + x2 = 6.984108947 Solving -4.666666667 + x2 = 6.984108947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + x2 = 6.984108947 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x2 = 6.984108947 + 4.666666667 x2 = 6.984108947 + 4.666666667 Combine like terms: 6.984108947 + 4.666666667 = 11.650775614 x2 = 11.650775614 Simplifying x2 = 11.650775614 Take the square root of each side: x = {-3.413323251, 3.413323251}Subproblem 2
x2 + -4.666666667 = -6.984108947 Simplifying x2 + -4.666666667 = -6.984108947 Reorder the terms: -4.666666667 + x2 = -6.984108947 Solving -4.666666667 + x2 = -6.984108947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + x2 = -6.984108947 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x2 = -6.984108947 + 4.666666667 x2 = -6.984108947 + 4.666666667 Combine like terms: -6.984108947 + 4.666666667 = -2.31744228 x2 = -2.31744228 Simplifying x2 = -2.31744228 Reorder the terms: 2.31744228 + x2 = -2.31744228 + 2.31744228 Combine like terms: -2.31744228 + 2.31744228 = 0.00000000 2.31744228 + x2 = 0.00000000 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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