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Simplifying 8x4 + -18x2 + -4 = 0 Reorder the terms: -4 + -18x2 + 8x4 = 0 Solving -4 + -18x2 + 8x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -9x2 + 4x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -9x2 + 4x4)' equal to zero and attempt to solve: Simplifying -2 + -9x2 + 4x4 = 0 Solving -2 + -9x2 + 4x4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.5 + -2.25x2 + x4 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2.25x2 + 0.5 + x4 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2.25x2 + x4 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2.25x2 + x4 = 0 + 0.5 -2.25x2 + x4 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2.25x2 + x4 = 0.5 The x term is -2.25x2. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x2 + 1.265625 + x4 = 0.5 + 1.265625 Reorder the terms: 1.265625 + -2.25x2 + x4 = 0.5 + 1.265625 Combine like terms: 0.5 + 1.265625 = 1.765625 1.265625 + -2.25x2 + x4 = 1.765625 Factor a perfect square on the left side: (x2 + -1.125)(x2 + -1.125) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (x2 + -1.125) equal to 1.328768227 and -1.328768227.Subproblem 1
x2 + -1.125 = 1.328768227 Simplifying x2 + -1.125 = 1.328768227 Reorder the terms: -1.125 + x2 = 1.328768227 Solving -1.125 + x2 = 1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x2 = 1.328768227 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x2 = 1.328768227 + 1.125 x2 = 1.328768227 + 1.125 Combine like terms: 1.328768227 + 1.125 = 2.453768227 x2 = 2.453768227 Simplifying x2 = 2.453768227 Take the square root of each side: x = {-1.566450838, 1.566450838}Subproblem 2
x2 + -1.125 = -1.328768227 Simplifying x2 + -1.125 = -1.328768227 Reorder the terms: -1.125 + x2 = -1.328768227 Solving -1.125 + x2 = -1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x2 = -1.328768227 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x2 = -1.328768227 + 1.125 x2 = -1.328768227 + 1.125 Combine like terms: -1.328768227 + 1.125 = -0.203768227 x2 = -0.203768227 Simplifying x2 = -0.203768227 Reorder the terms: 0.203768227 + x2 = -0.203768227 + 0.203768227 Combine like terms: -0.203768227 + 0.203768227 = 0.000000000 0.203768227 + 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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