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Simplifying 6c2 + 24c + -27 = 0 Reorder the terms: -27 + 24c + 6c2 = 0 Solving -27 + 24c + 6c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + 8c + 2c2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + 8c + 2c2)' equal to zero and attempt to solve: Simplifying -9 + 8c + 2c2 = 0 Solving -9 + 8c + 2c2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + 4c + c2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 4c + 4.5 + c2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 4c + c2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 4c + c2 = 0 + 4.5 4c + c2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 4c + c2 = 4.5 The c term is 4c. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4c + 4 + c2 = 4.5 + 4 Reorder the terms: 4 + 4c + c2 = 4.5 + 4 Combine like terms: 4.5 + 4 = 8.5 4 + 4c + c2 = 8.5 Factor a perfect square on the left side: (c + 2)(c + 2) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (c + 2) equal to 2.915475947 and -2.915475947.Subproblem 1
c + 2 = 2.915475947 Simplifying c + 2 = 2.915475947 Reorder the terms: 2 + c = 2.915475947 Solving 2 + c = 2.915475947 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = 2.915475947 + -2 Combine like terms: 2 + -2 = 0 0 + c = 2.915475947 + -2 c = 2.915475947 + -2 Combine like terms: 2.915475947 + -2 = 0.915475947 c = 0.915475947 Simplifying c = 0.915475947Subproblem 2
c + 2 = -2.915475947 Simplifying c + 2 = -2.915475947 Reorder the terms: 2 + c = -2.915475947 Solving 2 + c = -2.915475947 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = -2.915475947 + -2 Combine like terms: 2 + -2 = 0 0 + c = -2.915475947 + -2 c = -2.915475947 + -2 Combine like terms: -2.915475947 + -2 = -4.915475947 c = -4.915475947 Simplifying c = -4.915475947Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.915475947, -4.915475947}Solution
c = {0.915475947, -4.915475947}
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