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Simplifying 2x5 + 6x4 + 14x3 = 0 Reorder the terms: 14x3 + 6x4 + 2x5 = 0 Solving 14x3 + 6x4 + 2x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x3'. 2x3(7 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 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 '(7 + 3x + x2)' equal to zero and attempt to solve: Simplifying 7 + 3x + x2 = 0 Solving 7 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 3x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 3x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3x + x2 = 0 + -7 3x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 3x + x2 = -7 The x term is 3x. 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. 3x + 2.25 + x2 = -7 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -7 + 2.25 Combine like terms: -7 + 2.25 = -4.75 2.25 + 3x + x2 = -4.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -4.75 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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