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Simplifying 8(c2)((4c2) + 5c + 9) = 0 Reorder the terms: 8c2(9 + 5c + (4c2)) = 0 (9 * 8c2 + 5c * 8c2 + (4c2) * 8c2) = 0 (72c2 + 40c3 + 32c4) = 0 Solving 72c2 + 40c3 + 32c4 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '8c2'. 8c2(9 + 5c + 4c2) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'c2' equal to zero and attempt to solve: Simplifying c2 = 0 Solving c2 = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c2 = 0 Take the square root of each side: c = {0}Subproblem 2
Set the factor '(9 + 5c + 4c2)' equal to zero and attempt to solve: Simplifying 9 + 5c + 4c2 = 0 Solving 9 + 5c + 4c2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 1.25c + c2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 1.25c + -2.25 + c2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 1.25c + c2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 1.25c + c2 = 0 + -2.25 1.25c + c2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 1.25c + c2 = -2.25 The c term is 1.25c. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25c + 0.390625 + c2 = -2.25 + 0.390625 Reorder the terms: 0.390625 + 1.25c + c2 = -2.25 + 0.390625 Combine like terms: -2.25 + 0.390625 = -1.859375 0.390625 + 1.25c + c2 = -1.859375 Factor a perfect square on the left side: (c + 0.625)(c + 0.625) = -1.859375 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.Solution
c = {0}
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