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Simplifying 3x4 + -32x2 + 28 = 0 Reorder the terms: 28 + -32x2 + 3x4 = 0 Solving 28 + -32x2 + 3x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 9.333333333 + -10.66666667x2 + x4 = 0 Move the constant term to the right: Add '-9.333333333' to each side of the equation. 9.333333333 + -10.66666667x2 + -9.333333333 + x4 = 0 + -9.333333333 Reorder the terms: 9.333333333 + -9.333333333 + -10.66666667x2 + x4 = 0 + -9.333333333 Combine like terms: 9.333333333 + -9.333333333 = 0.000000000 0.000000000 + -10.66666667x2 + x4 = 0 + -9.333333333 -10.66666667x2 + x4 = 0 + -9.333333333 Combine like terms: 0 + -9.333333333 = -9.333333333 -10.66666667x2 + x4 = -9.333333333 The x term is -10.66666667x2. Take half its coefficient (-5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. -10.66666667x2 + 28.44444446 + x4 = -9.333333333 + 28.44444446 Reorder the terms: 28.44444446 + -10.66666667x2 + x4 = -9.333333333 + 28.44444446 Combine like terms: -9.333333333 + 28.44444446 = 19.111111127 28.44444446 + -10.66666667x2 + x4 = 19.111111127 Factor a perfect square on the left side: (x2 + -5.333333335)(x2 + -5.333333335) = 19.111111127 Calculate the square root of the right side: 4.371625685 Break this problem into two subproblems by setting (x2 + -5.333333335) equal to 4.371625685 and -4.371625685.Subproblem 1
x2 + -5.333333335 = 4.371625685 Simplifying x2 + -5.333333335 = 4.371625685 Reorder the terms: -5.333333335 + x2 = 4.371625685 Solving -5.333333335 + x2 = 4.371625685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x2 = 4.371625685 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x2 = 4.371625685 + 5.333333335 x2 = 4.371625685 + 5.333333335 Combine like terms: 4.371625685 + 5.333333335 = 9.70495902 x2 = 9.70495902 Simplifying x2 = 9.70495902 Take the square root of each side: x = {-3.115278321, 3.115278321}Subproblem 2
x2 + -5.333333335 = -4.371625685 Simplifying x2 + -5.333333335 = -4.371625685 Reorder the terms: -5.333333335 + x2 = -4.371625685 Solving -5.333333335 + x2 = -4.371625685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.333333335' to each side of the equation. -5.333333335 + 5.333333335 + x2 = -4.371625685 + 5.333333335 Combine like terms: -5.333333335 + 5.333333335 = 0.000000000 0.000000000 + x2 = -4.371625685 + 5.333333335 x2 = -4.371625685 + 5.333333335 Combine like terms: -4.371625685 + 5.333333335 = 0.96170765 x2 = 0.96170765 Simplifying x2 = 0.96170765 Take the square root of each side: x = {-0.980666941, 0.980666941}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.115278321, 3.115278321, -0.980666941, 0.980666941}
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