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Simplifying 3x4 + 9x2 + -6 = 0 Reorder the terms: -6 + 9x2 + 3x4 = 0 Solving -6 + 9x2 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 3x2 + x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + 3x2 + x4)' equal to zero and attempt to solve: Simplifying -2 + 3x2 + x4 = 0 Solving -2 + 3x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 3x2 + 2 + x4 = 0 + 2 Reorder the terms: -2 + 2 + 3x2 + x4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3x2 + x4 = 0 + 2 3x2 + x4 = 0 + 2 Combine like terms: 0 + 2 = 2 3x2 + x4 = 2 The x term is 3x2. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x2 + 2.25 + x4 = 2 + 2.25 Reorder the terms: 2.25 + 3x2 + x4 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + 3x2 + x4 = 4.25 Factor a perfect square on the left side: (x2 + 1.5)(x2 + 1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x2 + 1.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x2 + 1.5 = 2.061552813 Simplifying x2 + 1.5 = 2.061552813 Reorder the terms: 1.5 + x2 = 2.061552813 Solving 1.5 + x2 = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = 2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = 2.061552813 + -1.5 x2 = 2.061552813 + -1.5 Combine like terms: 2.061552813 + -1.5 = 0.561552813 x2 = 0.561552813 Simplifying x2 = 0.561552813 Take the square root of each side: x = {-0.749368276, 0.749368276}Subproblem 2
x2 + 1.5 = -2.061552813 Simplifying x2 + 1.5 = -2.061552813 Reorder the terms: 1.5 + x2 = -2.061552813 Solving 1.5 + x2 = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = -2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = -2.061552813 + -1.5 x2 = -2.061552813 + -1.5 Combine like terms: -2.061552813 + -1.5 = -3.561552813 x2 = -3.561552813 Simplifying x2 = -3.561552813 Reorder the terms: 3.561552813 + x2 = -3.561552813 + 3.561552813 Combine like terms: -3.561552813 + 3.561552813 = 0.000000000 3.561552813 + 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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