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Simplifying (c + 3) + -1c(c + -4) = 9c + -16 Reorder the terms: (3 + c) + -1c(c + -4) = 9c + -16 Remove parenthesis around (3 + c) 3 + c + -1c(c + -4) = 9c + -16 Reorder the terms: 3 + c + -1c(-4 + c) = 9c + -16 3 + c + (-4 * -1c + c * -1c) = 9c + -16 3 + c + (4c + -1c2) = 9c + -16 Combine like terms: c + 4c = 5c 3 + 5c + -1c2 = 9c + -16 Reorder the terms: 3 + 5c + -1c2 = -16 + 9c Solving 3 + 5c + -1c2 = -16 + 9c Solving for variable 'c'. Reorder the terms: 3 + 16 + 5c + -9c + -1c2 = -16 + 9c + 16 + -9c Combine like terms: 3 + 16 = 19 19 + 5c + -9c + -1c2 = -16 + 9c + 16 + -9c Combine like terms: 5c + -9c = -4c 19 + -4c + -1c2 = -16 + 9c + 16 + -9c Reorder the terms: 19 + -4c + -1c2 = -16 + 16 + 9c + -9c Combine like terms: -16 + 16 = 0 19 + -4c + -1c2 = 0 + 9c + -9c 19 + -4c + -1c2 = 9c + -9c Combine like terms: 9c + -9c = 0 19 + -4c + -1c2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -19 + 4c + c2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + 4c + 19 + c2 = 0 + 19 Reorder the terms: -19 + 19 + 4c + c2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 4c + c2 = 0 + 19 4c + c2 = 0 + 19 Combine like terms: 0 + 19 = 19 4c + c2 = 19 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 = 19 + 4 Reorder the terms: 4 + 4c + c2 = 19 + 4 Combine like terms: 19 + 4 = 23 4 + 4c + c2 = 23 Factor a perfect square on the left side: (c + 2)(c + 2) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (c + 2) equal to 4.795831523 and -4.795831523.Subproblem 1
c + 2 = 4.795831523 Simplifying c + 2 = 4.795831523 Reorder the terms: 2 + c = 4.795831523 Solving 2 + c = 4.795831523 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 = 4.795831523 + -2 Combine like terms: 2 + -2 = 0 0 + c = 4.795831523 + -2 c = 4.795831523 + -2 Combine like terms: 4.795831523 + -2 = 2.795831523 c = 2.795831523 Simplifying c = 2.795831523Subproblem 2
c + 2 = -4.795831523 Simplifying c + 2 = -4.795831523 Reorder the terms: 2 + c = -4.795831523 Solving 2 + c = -4.795831523 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 = -4.795831523 + -2 Combine like terms: 2 + -2 = 0 0 + c = -4.795831523 + -2 c = -4.795831523 + -2 Combine like terms: -4.795831523 + -2 = -6.795831523 c = -6.795831523 Simplifying c = -6.795831523Solution
The solution to the problem is based on the solutions from the subproblems. c = {2.795831523, -6.795831523}
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