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Simplifying 5(c + -6) * c + 11 = 24 Reorder the terms: 5(-6 + c) * c + 11 = 24 Reorder the terms for easier multiplication: 5c(-6 + c) + 11 = 24 (-6 * 5c + c * 5c) + 11 = 24 (-30c + 5c2) + 11 = 24 Reorder the terms: 11 + -30c + 5c2 = 24 Solving 11 + -30c + 5c2 = 24 Solving for variable 'c'. Reorder the terms: 11 + -24 + -30c + 5c2 = 24 + -24 Combine like terms: 11 + -24 = -13 -13 + -30c + 5c2 = 24 + -24 Combine like terms: 24 + -24 = 0 -13 + -30c + 5c2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + -6c + c2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -6c + 2.6 + c2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -6c + c2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -6c + c2 = 0 + 2.6 -6c + c2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -6c + c2 = 2.6 The c term is -6c. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6c + 9 + c2 = 2.6 + 9 Reorder the terms: 9 + -6c + c2 = 2.6 + 9 Combine like terms: 2.6 + 9 = 11.6 9 + -6c + c2 = 11.6 Factor a perfect square on the left side: (c + -3)(c + -3) = 11.6 Calculate the square root of the right side: 3.405877273 Break this problem into two subproblems by setting (c + -3) equal to 3.405877273 and -3.405877273.Subproblem 1
c + -3 = 3.405877273 Simplifying c + -3 = 3.405877273 Reorder the terms: -3 + c = 3.405877273 Solving -3 + c = 3.405877273 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + c = 3.405877273 + 3 Combine like terms: -3 + 3 = 0 0 + c = 3.405877273 + 3 c = 3.405877273 + 3 Combine like terms: 3.405877273 + 3 = 6.405877273 c = 6.405877273 Simplifying c = 6.405877273Subproblem 2
c + -3 = -3.405877273 Simplifying c + -3 = -3.405877273 Reorder the terms: -3 + c = -3.405877273 Solving -3 + c = -3.405877273 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + c = -3.405877273 + 3 Combine like terms: -3 + 3 = 0 0 + c = -3.405877273 + 3 c = -3.405877273 + 3 Combine like terms: -3.405877273 + 3 = -0.405877273 c = -0.405877273 Simplifying c = -0.405877273Solution
The solution to the problem is based on the solutions from the subproblems. c = {6.405877273, -0.405877273}
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