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Simplifying 21x6 + 8x5 + 24x4 = 0 Reorder the terms: 24x4 + 8x5 + 21x6 = 0 Solving 24x4 + 8x5 + 21x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x4'. x4(24 + 8x + 21x2) = 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 '(24 + 8x + 21x2)' equal to zero and attempt to solve: Simplifying 24 + 8x + 21x2 = 0 Solving 24 + 8x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 1.142857143 + 0.380952381x + x2 = 0 Move the constant term to the right: Add '-1.142857143' to each side of the equation. 1.142857143 + 0.380952381x + -1.142857143 + x2 = 0 + -1.142857143 Reorder the terms: 1.142857143 + -1.142857143 + 0.380952381x + x2 = 0 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + 0.380952381x + x2 = 0 + -1.142857143 0.380952381x + x2 = 0 + -1.142857143 Combine like terms: 0 + -1.142857143 = -1.142857143 0.380952381x + x2 = -1.142857143 The x term is 0.380952381x. Take half its coefficient (0.1904761905). Square it (0.03628117915) and add it to both sides. Add '0.03628117915' to each side of the equation. 0.380952381x + 0.03628117915 + x2 = -1.142857143 + 0.03628117915 Reorder the terms: 0.03628117915 + 0.380952381x + x2 = -1.142857143 + 0.03628117915 Combine like terms: -1.142857143 + 0.03628117915 = -1.10657596385 0.03628117915 + 0.380952381x + x2 = -1.10657596385 Factor a perfect square on the left side: (x + 0.1904761905)(x + 0.1904761905) = -1.10657596385 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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