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Simplifying c(c + 2) + (c + 4) = 27 Reorder the terms: c(2 + c) + (c + 4) = 27 (2 * c + c * c) + (c + 4) = 27 (2c + c2) + (c + 4) = 27 Reorder the terms: 2c + c2 + (4 + c) = 27 Remove parenthesis around (4 + c) 2c + c2 + 4 + c = 27 Reorder the terms: 4 + 2c + c + c2 = 27 Combine like terms: 2c + c = 3c 4 + 3c + c2 = 27 Solving 4 + 3c + c2 = 27 Solving for variable 'c'. Reorder the terms: 4 + -27 + 3c + c2 = 27 + -27 Combine like terms: 4 + -27 = -23 -23 + 3c + c2 = 27 + -27 Combine like terms: 27 + -27 = 0 -23 + 3c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 3c + 23 + c2 = 0 + 23 Reorder the terms: -23 + 23 + 3c + c2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 3c + c2 = 0 + 23 3c + c2 = 0 + 23 Combine like terms: 0 + 23 = 23 3c + c2 = 23 The c term is 3c. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3c + 2.25 + c2 = 23 + 2.25 Reorder the terms: 2.25 + 3c + c2 = 23 + 2.25 Combine like terms: 23 + 2.25 = 25.25 2.25 + 3c + c2 = 25.25 Factor a perfect square on the left side: (c + 1.5)(c + 1.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (c + 1.5) equal to 5.024937811 and -5.024937811.Subproblem 1
c + 1.5 = 5.024937811 Simplifying c + 1.5 = 5.024937811 Reorder the terms: 1.5 + c = 5.024937811 Solving 1.5 + c = 5.024937811 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + c = 5.024937811 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = 5.024937811 + -1.5 c = 5.024937811 + -1.5 Combine like terms: 5.024937811 + -1.5 = 3.524937811 c = 3.524937811 Simplifying c = 3.524937811Subproblem 2
c + 1.5 = -5.024937811 Simplifying c + 1.5 = -5.024937811 Reorder the terms: 1.5 + c = -5.024937811 Solving 1.5 + c = -5.024937811 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + c = -5.024937811 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = -5.024937811 + -1.5 c = -5.024937811 + -1.5 Combine like terms: -5.024937811 + -1.5 = -6.524937811 c = -6.524937811 Simplifying c = -6.524937811Solution
The solution to the problem is based on the solutions from the subproblems. c = {3.524937811, -6.524937811}
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