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Simplifying -4c(-9c2 + 5c + 8) = 0 Reorder the terms: -4c(8 + 5c + -9c2) = 0 (8 * -4c + 5c * -4c + -9c2 * -4c) = 0 (-32c + -20c2 + 36c3) = 0 Solving -32c + -20c2 + 36c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '4c'. 4c(-8 + -5c + 9c2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'c' equal to zero and attempt to solve: Simplifying c = 0 Solving c = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c = 0Subproblem 2
Set the factor '(-8 + -5c + 9c2)' equal to zero and attempt to solve: Simplifying -8 + -5c + 9c2 = 0 Solving -8 + -5c + 9c2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + -0.5555555556c + c2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -0.5555555556c + 0.8888888889 + c2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -0.5555555556c + c2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -0.5555555556c + c2 = 0 + 0.8888888889 -0.5555555556c + c2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -0.5555555556c + c2 = 0.8888888889 The c term is -0.5555555556c. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556c + 0.07716049384 + c2 = 0.8888888889 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556c + c2 = 0.8888888889 + 0.07716049384 Combine like terms: 0.8888888889 + 0.07716049384 = 0.96604938274 0.07716049384 + -0.5555555556c + c2 = 0.96604938274 Factor a perfect square on the left side: (c + -0.2777777778)(c + -0.2777777778) = 0.96604938274 Calculate the square root of the right side: 0.982878112 Break this problem into two subproblems by setting (c + -0.2777777778) equal to 0.982878112 and -0.982878112.Subproblem 1
c + -0.2777777778 = 0.982878112 Simplifying c + -0.2777777778 = 0.982878112 Reorder the terms: -0.2777777778 + c = 0.982878112 Solving -0.2777777778 + c = 0.982878112 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + c = 0.982878112 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + c = 0.982878112 + 0.2777777778 c = 0.982878112 + 0.2777777778 Combine like terms: 0.982878112 + 0.2777777778 = 1.2606558898 c = 1.2606558898 Simplifying c = 1.2606558898Subproblem 2
c + -0.2777777778 = -0.982878112 Simplifying c + -0.2777777778 = -0.982878112 Reorder the terms: -0.2777777778 + c = -0.982878112 Solving -0.2777777778 + c = -0.982878112 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + c = -0.982878112 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + c = -0.982878112 + 0.2777777778 c = -0.982878112 + 0.2777777778 Combine like terms: -0.982878112 + 0.2777777778 = -0.7051003342 c = -0.7051003342 Simplifying c = -0.7051003342Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.2606558898, -0.7051003342}Solution
c = {0, 1.2606558898, -0.7051003342}
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