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Simplifying 4x6 + -3x5 + 14x4 = 0 Reorder the terms: 14x4 + -3x5 + 4x6 = 0 Solving 14x4 + -3x5 + 4x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x4'. x4(14 + -3x + 4x2) = 0Subproblem 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 '(14 + -3x + 4x2)' equal to zero and attempt to solve: Simplifying 14 + -3x + 4x2 = 0 Solving 14 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.5 + -0.75x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -0.75x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -0.75x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -0.75x + x2 = 0 + -3.5 -0.75x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -0.75x + x2 = -3.5 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -3.5 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -3.5 + 0.140625 Combine like terms: -3.5 + 0.140625 = -3.359375 0.140625 + -0.75x + x2 = -3.359375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -3.359375 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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