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Simplifying 5x4 + -30x2 + 1 = 0 Reorder the terms: 1 + -30x2 + 5x4 = 0 Solving 1 + -30x2 + 5x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -6x2 + x4 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -6x2 + -0.2 + x4 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -6x2 + x4 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -6x2 + x4 = 0 + -0.2 -6x2 + x4 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -6x2 + x4 = -0.2 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 = -0.2 + 9 Reorder the terms: 9 + -6x2 + x4 = -0.2 + 9 Combine like terms: -0.2 + 9 = 8.8 9 + -6x2 + x4 = 8.8 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 8.8 Calculate the square root of the right side: 2.966479395 Break this problem into two subproblems by setting (x2 + -3) equal to 2.966479395 and -2.966479395.Subproblem 1
x2 + -3 = 2.966479395 Simplifying x2 + -3 = 2.966479395 Reorder the terms: -3 + x2 = 2.966479395 Solving -3 + x2 = 2.966479395 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 = 2.966479395 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 2.966479395 + 3 x2 = 2.966479395 + 3 Combine like terms: 2.966479395 + 3 = 5.966479395 x2 = 5.966479395 Simplifying x2 = 5.966479395 Take the square root of each side: x = {-2.442637794, 2.442637794}Subproblem 2
x2 + -3 = -2.966479395 Simplifying x2 + -3 = -2.966479395 Reorder the terms: -3 + x2 = -2.966479395 Solving -3 + x2 = -2.966479395 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 = -2.966479395 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -2.966479395 + 3 x2 = -2.966479395 + 3 Combine like terms: -2.966479395 + 3 = 0.033520605 x2 = 0.033520605 Simplifying x2 = 0.033520605 Take the square root of each side: x = {-0.183086332, 0.183086332}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.442637794, 2.442637794, -0.183086332, 0.183086332}
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