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Simplifying 4c2 + 19c = 21 Reorder the terms: 19c + 4c2 = 21 Solving 19c + 4c2 = 21 Solving for variable 'c'. Reorder the terms: -21 + 19c + 4c2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 19c + 4c2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + 4.75c + c2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 4.75c + 5.25 + c2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 4.75c + c2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 4.75c + c2 = 0 + 5.25 4.75c + c2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 4.75c + c2 = 5.25 The c term is 4.75c. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75c + 5.640625 + c2 = 5.25 + 5.640625 Reorder the terms: 5.640625 + 4.75c + c2 = 5.25 + 5.640625 Combine like terms: 5.25 + 5.640625 = 10.890625 5.640625 + 4.75c + c2 = 10.890625 Factor a perfect square on the left side: (c + 2.375)(c + 2.375) = 10.890625 Calculate the square root of the right side: 3.300094696 Break this problem into two subproblems by setting (c + 2.375) equal to 3.300094696 and -3.300094696.Subproblem 1
c + 2.375 = 3.300094696 Simplifying c + 2.375 = 3.300094696 Reorder the terms: 2.375 + c = 3.300094696 Solving 2.375 + c = 3.300094696 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + c = 3.300094696 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + c = 3.300094696 + -2.375 c = 3.300094696 + -2.375 Combine like terms: 3.300094696 + -2.375 = 0.925094696 c = 0.925094696 Simplifying c = 0.925094696Subproblem 2
c + 2.375 = -3.300094696 Simplifying c + 2.375 = -3.300094696 Reorder the terms: 2.375 + c = -3.300094696 Solving 2.375 + c = -3.300094696 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + c = -3.300094696 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + c = -3.300094696 + -2.375 c = -3.300094696 + -2.375 Combine like terms: -3.300094696 + -2.375 = -5.675094696 c = -5.675094696 Simplifying c = -5.675094696Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.925094696, -5.675094696}
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