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Simplifying (2(3x4 + 18x2 + -16)) = 0 Reorder the terms: (2(-16 + 18x2 + 3x4)) = 0 ((-16 * 2 + 18x2 * 2 + 3x4 * 2)) = 0 ((-32 + 36x2 + 6x4)) = 0 (-32 + 36x2 + 6x4) = 0 Remove parenthesis around (-32 + 36x2 + 6x4) -32 + 36x2 + 6x4 = 0 Solving -32 + 36x2 + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + 18x2 + 3x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + 18x2 + 3x4)' equal to zero and attempt to solve: Simplifying -16 + 18x2 + 3x4 = 0 Solving -16 + 18x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + 6x2 + x4 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + 6x2 + 5.333333333 + x4 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + 6x2 + x4 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + 6x2 + x4 = 0 + 5.333333333 6x2 + x4 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 6x2 + x4 = 5.333333333 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 = 5.333333333 + 9 Reorder the terms: 9 + 6x2 + x4 = 5.333333333 + 9 Combine like terms: 5.333333333 + 9 = 14.333333333 9 + 6x2 + x4 = 14.333333333 Factor a perfect square on the left side: (x2 + 3)(x2 + 3) = 14.333333333 Calculate the square root of the right side: 3.785938897 Break this problem into two subproblems by setting (x2 + 3) equal to 3.785938897 and -3.785938897.Subproblem 1
x2 + 3 = 3.785938897 Simplifying x2 + 3 = 3.785938897 Reorder the terms: 3 + x2 = 3.785938897 Solving 3 + x2 = 3.785938897 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 = 3.785938897 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = 3.785938897 + -3 x2 = 3.785938897 + -3 Combine like terms: 3.785938897 + -3 = 0.785938897 x2 = 0.785938897 Simplifying x2 = 0.785938897 Take the square root of each side: x = {-0.886531949, 0.886531949}Subproblem 2
x2 + 3 = -3.785938897 Simplifying x2 + 3 = -3.785938897 Reorder the terms: 3 + x2 = -3.785938897 Solving 3 + x2 = -3.785938897 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 = -3.785938897 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = -3.785938897 + -3 x2 = -3.785938897 + -3 Combine like terms: -3.785938897 + -3 = -6.785938897 x2 = -6.785938897 Simplifying x2 = -6.785938897 Reorder the terms: 6.785938897 + x2 = -6.785938897 + 6.785938897 Combine like terms: -6.785938897 + 6.785938897 = 0.000000000 6.785938897 + 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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