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Simplifying 6(c + 5) * c = 4 Reorder the terms: 6(5 + c) * c = 4 Reorder the terms for easier multiplication: 6c(5 + c) = 4 (5 * 6c + c * 6c) = 4 (30c + 6c2) = 4 Solving 30c + 6c2 = 4 Solving for variable 'c'. Reorder the terms: -4 + 30c + 6c2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 30c + 6c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 15c + 3c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 15c + 3c2)' equal to zero and attempt to solve: Simplifying -2 + 15c + 3c2 = 0 Solving -2 + 15c + 3c2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + 5c + c2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 5c + 0.6666666667 + c2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 5c + c2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 5c + c2 = 0 + 0.6666666667 5c + c2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 5c + c2 = 0.6666666667 The c term is 5c. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5c + 6.25 + c2 = 0.6666666667 + 6.25 Reorder the terms: 6.25 + 5c + c2 = 0.6666666667 + 6.25 Combine like terms: 0.6666666667 + 6.25 = 6.9166666667 6.25 + 5c + c2 = 6.9166666667 Factor a perfect square on the left side: (c + 2.5)(c + 2.5) = 6.9166666667 Calculate the square root of the right side: 2.62995564 Break this problem into two subproblems by setting (c + 2.5) equal to 2.62995564 and -2.62995564.Subproblem 1
c + 2.5 = 2.62995564 Simplifying c + 2.5 = 2.62995564 Reorder the terms: 2.5 + c = 2.62995564 Solving 2.5 + c = 2.62995564 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + c = 2.62995564 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + c = 2.62995564 + -2.5 c = 2.62995564 + -2.5 Combine like terms: 2.62995564 + -2.5 = 0.12995564 c = 0.12995564 Simplifying c = 0.12995564Subproblem 2
c + 2.5 = -2.62995564 Simplifying c + 2.5 = -2.62995564 Reorder the terms: 2.5 + c = -2.62995564 Solving 2.5 + c = -2.62995564 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + c = -2.62995564 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + c = -2.62995564 + -2.5 c = -2.62995564 + -2.5 Combine like terms: -2.62995564 + -2.5 = -5.12995564 c = -5.12995564 Simplifying c = -5.12995564Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.12995564, -5.12995564}Solution
c = {0.12995564, -5.12995564}
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