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Simplifying 48 + -1(3c + 4) = 4(c + 7) * c Reorder the terms: 48 + -1(4 + 3c) = 4(c + 7) * c 48 + (4 * -1 + 3c * -1) = 4(c + 7) * c 48 + (-4 + -3c) = 4(c + 7) * c Combine like terms: 48 + -4 = 44 44 + -3c = 4(c + 7) * c Reorder the terms: 44 + -3c = 4(7 + c) * c Reorder the terms for easier multiplication: 44 + -3c = 4c(7 + c) 44 + -3c = (7 * 4c + c * 4c) 44 + -3c = (28c + 4c2) Solving 44 + -3c = 28c + 4c2 Solving for variable 'c'. Combine like terms: -3c + -28c = -31c 44 + -31c + -4c2 = 28c + 4c2 + -28c + -4c2 Reorder the terms: 44 + -31c + -4c2 = 28c + -28c + 4c2 + -4c2 Combine like terms: 28c + -28c = 0 44 + -31c + -4c2 = 0 + 4c2 + -4c2 44 + -31c + -4c2 = 4c2 + -4c2 Combine like terms: 4c2 + -4c2 = 0 44 + -31c + -4c2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -11 + 7.75c + c2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 7.75c + 11 + c2 = 0 + 11 Reorder the terms: -11 + 11 + 7.75c + c2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 7.75c + c2 = 0 + 11 7.75c + c2 = 0 + 11 Combine like terms: 0 + 11 = 11 7.75c + c2 = 11 The c term is 7.75c. Take half its coefficient (3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. 7.75c + 15.015625 + c2 = 11 + 15.015625 Reorder the terms: 15.015625 + 7.75c + c2 = 11 + 15.015625 Combine like terms: 11 + 15.015625 = 26.015625 15.015625 + 7.75c + c2 = 26.015625 Factor a perfect square on the left side: (c + 3.875)(c + 3.875) = 26.015625 Calculate the square root of the right side: 5.100551441 Break this problem into two subproblems by setting (c + 3.875) equal to 5.100551441 and -5.100551441.Subproblem 1
c + 3.875 = 5.100551441 Simplifying c + 3.875 = 5.100551441 Reorder the terms: 3.875 + c = 5.100551441 Solving 3.875 + c = 5.100551441 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + c = 5.100551441 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + c = 5.100551441 + -3.875 c = 5.100551441 + -3.875 Combine like terms: 5.100551441 + -3.875 = 1.225551441 c = 1.225551441 Simplifying c = 1.225551441Subproblem 2
c + 3.875 = -5.100551441 Simplifying c + 3.875 = -5.100551441 Reorder the terms: 3.875 + c = -5.100551441 Solving 3.875 + c = -5.100551441 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3.875' to each side of the equation. 3.875 + -3.875 + c = -5.100551441 + -3.875 Combine like terms: 3.875 + -3.875 = 0.000 0.000 + c = -5.100551441 + -3.875 c = -5.100551441 + -3.875 Combine like terms: -5.100551441 + -3.875 = -8.975551441 c = -8.975551441 Simplifying c = -8.975551441Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.225551441, -8.975551441}
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