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Simplifying 6x4 + -40x2 + 9 = 0 Reorder the terms: 9 + -40x2 + 6x4 = 0 Solving 9 + -40x2 + 6x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.5 + -6.666666667x2 + x4 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -6.666666667x2 + -1.5 + x4 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -6.666666667x2 + x4 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -6.666666667x2 + x4 = 0 + -1.5 -6.666666667x2 + x4 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -6.666666667x2 + x4 = -1.5 The x term is -6.666666667x2. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667x2 + 11.11111112 + x4 = -1.5 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x2 + x4 = -1.5 + 11.11111112 Combine like terms: -1.5 + 11.11111112 = 9.61111112 11.11111112 + -6.666666667x2 + x4 = 9.61111112 Factor a perfect square on the left side: (x2 + -3.333333334)(x2 + -3.333333334) = 9.61111112 Calculate the square root of the right side: 3.100179208 Break this problem into two subproblems by setting (x2 + -3.333333334) equal to 3.100179208 and -3.100179208.Subproblem 1
x2 + -3.333333334 = 3.100179208 Simplifying x2 + -3.333333334 = 3.100179208 Reorder the terms: -3.333333334 + x2 = 3.100179208 Solving -3.333333334 + x2 = 3.100179208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x2 = 3.100179208 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x2 = 3.100179208 + 3.333333334 x2 = 3.100179208 + 3.333333334 Combine like terms: 3.100179208 + 3.333333334 = 6.433512542 x2 = 6.433512542 Simplifying x2 = 6.433512542 Take the square root of each side: x = {-2.536436978, 2.536436978}Subproblem 2
x2 + -3.333333334 = -3.100179208 Simplifying x2 + -3.333333334 = -3.100179208 Reorder the terms: -3.333333334 + x2 = -3.100179208 Solving -3.333333334 + x2 = -3.100179208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x2 = -3.100179208 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x2 = -3.100179208 + 3.333333334 x2 = -3.100179208 + 3.333333334 Combine like terms: -3.100179208 + 3.333333334 = 0.233154126 x2 = 0.233154126 Simplifying x2 = 0.233154126 Take the square root of each side: x = {-0.482860359, 0.482860359}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.536436978, 2.536436978, -0.482860359, 0.482860359}
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