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Simplifying 4x6 + 16x5 + 42x4 = 0 Reorder the terms: 42x4 + 16x5 + 4x6 = 0 Solving 42x4 + 16x5 + 4x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x4'. 2x4(21 + 8x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(21 + 8x + 2x2)' equal to zero and attempt to solve: Simplifying 21 + 8x + 2x2 = 0 Solving 21 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10.5 + 4x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + 4x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + 4x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + 4x + x2 = 0 + -10.5 4x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 4x + x2 = -10.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -10.5 + 4 Reorder the terms: 4 + 4x + x2 = -10.5 + 4 Combine like terms: -10.5 + 4 = -6.5 4 + 4x + x2 = -6.5 Factor a perfect square on the left side: (x + 2)(x + 2) = -6.5 Can't calculate square root of the right side. 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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