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Simplifying 3x4 + 30x2 + -27 = 0 Reorder the terms: -27 + 30x2 + 3x4 = 0 Solving -27 + 30x2 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + 10x2 + x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + 10x2 + x4)' equal to zero and attempt to solve: Simplifying -9 + 10x2 + x4 = 0 Solving -9 + 10x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 10x2 + 9 + x4 = 0 + 9 Reorder the terms: -9 + 9 + 10x2 + x4 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 10x2 + x4 = 0 + 9 10x2 + x4 = 0 + 9 Combine like terms: 0 + 9 = 9 10x2 + x4 = 9 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 = 9 + 25 Reorder the terms: 25 + 10x2 + x4 = 9 + 25 Combine like terms: 9 + 25 = 34 25 + 10x2 + x4 = 34 Factor a perfect square on the left side: (x2 + 5)(x2 + 5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x2 + 5) equal to 5.830951895 and -5.830951895.Subproblem 1
x2 + 5 = 5.830951895 Simplifying x2 + 5 = 5.830951895 Reorder the terms: 5 + x2 = 5.830951895 Solving 5 + x2 = 5.830951895 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 = 5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = 5.830951895 + -5 x2 = 5.830951895 + -5 Combine like terms: 5.830951895 + -5 = 0.830951895 x2 = 0.830951895 Simplifying x2 = 0.830951895 Take the square root of each side: x = {-0.911565628, 0.911565628}Subproblem 2
x2 + 5 = -5.830951895 Simplifying x2 + 5 = -5.830951895 Reorder the terms: 5 + x2 = -5.830951895 Solving 5 + x2 = -5.830951895 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 = -5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = -5.830951895 + -5 x2 = -5.830951895 + -5 Combine like terms: -5.830951895 + -5 = -10.830951895 x2 = -10.830951895 Simplifying x2 = -10.830951895 Reorder the terms: 10.830951895 + x2 = -10.830951895 + 10.830951895 Combine like terms: -10.830951895 + 10.830951895 = 0.000000000 10.830951895 + 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. 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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