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Simplifying 8(c + 4) * c = 3 Reorder the terms: 8(4 + c) * c = 3 Reorder the terms for easier multiplication: 8c(4 + c) = 3 (4 * 8c + c * 8c) = 3 (32c + 8c2) = 3 Solving 32c + 8c2 = 3 Solving for variable 'c'. Reorder the terms: -3 + 32c + 8c2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 32c + 8c2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + 4c + c2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 4c + 0.375 + c2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 4c + c2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 4c + c2 = 0 + 0.375 4c + c2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 4c + c2 = 0.375 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 = 0.375 + 4 Reorder the terms: 4 + 4c + c2 = 0.375 + 4 Combine like terms: 0.375 + 4 = 4.375 4 + 4c + c2 = 4.375 Factor a perfect square on the left side: (c + 2)(c + 2) = 4.375 Calculate the square root of the right side: 2.091650066 Break this problem into two subproblems by setting (c + 2) equal to 2.091650066 and -2.091650066.Subproblem 1
c + 2 = 2.091650066 Simplifying c + 2 = 2.091650066 Reorder the terms: 2 + c = 2.091650066 Solving 2 + c = 2.091650066 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 = 2.091650066 + -2 Combine like terms: 2 + -2 = 0 0 + c = 2.091650066 + -2 c = 2.091650066 + -2 Combine like terms: 2.091650066 + -2 = 0.091650066 c = 0.091650066 Simplifying c = 0.091650066Subproblem 2
c + 2 = -2.091650066 Simplifying c + 2 = -2.091650066 Reorder the terms: 2 + c = -2.091650066 Solving 2 + c = -2.091650066 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 = -2.091650066 + -2 Combine like terms: 2 + -2 = 0 0 + c = -2.091650066 + -2 c = -2.091650066 + -2 Combine like terms: -2.091650066 + -2 = -4.091650066 c = -4.091650066 Simplifying c = -4.091650066Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.091650066, -4.091650066}
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