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Simplifying 3x4 + 30x2 + -1 = 0 Reorder the terms: -1 + 30x2 + 3x4 = 0 Solving -1 + 30x2 + 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'. -0.3333333333 + 10x2 + x4 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 10x2 + 0.3333333333 + x4 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 10x2 + x4 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 10x2 + x4 = 0 + 0.3333333333 10x2 + x4 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 10x2 + x4 = 0.3333333333 The x term is 10x2. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x2 + 25 + x4 = 0.3333333333 + 25 Reorder the terms: 25 + 10x2 + x4 = 0.3333333333 + 25 Combine like terms: 0.3333333333 + 25 = 25.3333333333 25 + 10x2 + x4 = 25.3333333333 Factor a perfect square on the left side: (x2 + 5)(x2 + 5) = 25.3333333333 Calculate the square root of the right side: 5.033222957 Break this problem into two subproblems by setting (x2 + 5) equal to 5.033222957 and -5.033222957.Subproblem 1
x2 + 5 = 5.033222957 Simplifying x2 + 5 = 5.033222957 Reorder the terms: 5 + x2 = 5.033222957 Solving 5 + x2 = 5.033222957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x2 = 5.033222957 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = 5.033222957 + -5 x2 = 5.033222957 + -5 Combine like terms: 5.033222957 + -5 = 0.033222957 x2 = 0.033222957 Simplifying x2 = 0.033222957 Take the square root of each side: x = {-0.182271657, 0.182271657}Subproblem 2
x2 + 5 = -5.033222957 Simplifying x2 + 5 = -5.033222957 Reorder the terms: 5 + x2 = -5.033222957 Solving 5 + x2 = -5.033222957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x2 = -5.033222957 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = -5.033222957 + -5 x2 = -5.033222957 + -5 Combine like terms: -5.033222957 + -5 = -10.033222957 x2 = -10.033222957 Simplifying x2 = -10.033222957 Reorder the terms: 10.033222957 + x2 = -10.033222957 + 10.033222957 Combine like terms: -10.033222957 + 10.033222957 = 0.000000000 10.033222957 + 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.
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