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Simplifying 6x4 + -36x2 + 32 = 0 Reorder the terms: 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 = 3.666666667 9 + -6x2 + x4 = 3.666666667 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 3.666666667 Calculate the square root of the right side: 1.914854216 Break this problem into two subproblems by setting (x2 + -3) equal to 1.914854216 and -1.914854216.Subproblem 1
x2 + -3 = 1.914854216 Simplifying x2 + -3 = 1.914854216 Reorder the terms: -3 + x2 = 1.914854216 Solving -3 + x2 = 1.914854216 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 = 1.914854216 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 1.914854216 + 3 x2 = 1.914854216 + 3 Combine like terms: 1.914854216 + 3 = 4.914854216 x2 = 4.914854216 Simplifying x2 = 4.914854216 Take the square root of each side: x = {-2.216947049, 2.216947049}Subproblem 2
x2 + -3 = -1.914854216 Simplifying x2 + -3 = -1.914854216 Reorder the terms: -3 + x2 = -1.914854216 Solving -3 + x2 = -1.914854216 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 = -1.914854216 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -1.914854216 + 3 x2 = -1.914854216 + 3 Combine like terms: -1.914854216 + 3 = 1.085145784 x2 = 1.085145784 Simplifying x2 = 1.085145784 Take the square root of each side: x = {-1.041703309, 1.041703309}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.216947049, 2.216947049, -1.041703309, 1.041703309}Solution
x = {-2.216947049, 2.216947049, -1.041703309, 1.041703309}
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