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Simplifying -12c4p + -20c3p + -16c2p = 0 Reorder the terms: -16c2p + -20c3p + -12c4p = 0 Solving -16c2p + -20c3p + -12c4p = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '-4c2p'. -4c2p(4 + 5c + 3c2) = 0 Ignore the factor -4.Subproblem 1
Set the factor 'c2p' equal to zero and attempt to solve: Simplifying c2p = 0 Solving c2p = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c2p = 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 '(4 + 5c + 3c2)' equal to zero and attempt to solve: Simplifying 4 + 5c + 3c2 = 0 Solving 4 + 5c + 3c2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 1.666666667c + c2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 1.666666667c + -1.333333333 + c2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 1.666666667c + c2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 1.666666667c + c2 = 0 + -1.333333333 1.666666667c + c2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 1.666666667c + c2 = -1.333333333 The c term is 1.666666667c. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667c + 0.6944444447 + c2 = -1.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667c + c2 = -1.333333333 + 0.6944444447 Combine like terms: -1.333333333 + 0.6944444447 = -0.6388888883 0.6944444447 + 1.666666667c + c2 = -0.6388888883 Factor a perfect square on the left side: (c + 0.8333333335)(c + 0.8333333335) = -0.6388888883 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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