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Simplifying c2 + 18c + -3 = 0 Reorder the terms: -3 + 18c + c2 = 0 Solving -3 + 18c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 18c + 3 + c2 = 0 + 3 Reorder the terms: -3 + 3 + 18c + c2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 18c + c2 = 0 + 3 18c + c2 = 0 + 3 Combine like terms: 0 + 3 = 3 18c + c2 = 3 The c term is 18c. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18c + 81 + c2 = 3 + 81 Reorder the terms: 81 + 18c + c2 = 3 + 81 Combine like terms: 3 + 81 = 84 81 + 18c + c2 = 84 Factor a perfect square on the left side: (c + 9)(c + 9) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (c + 9) equal to 9.16515139 and -9.16515139.Subproblem 1
c + 9 = 9.16515139 Simplifying c + 9 = 9.16515139 Reorder the terms: 9 + c = 9.16515139 Solving 9 + c = 9.16515139 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + c = 9.16515139 + -9 Combine like terms: 9 + -9 = 0 0 + c = 9.16515139 + -9 c = 9.16515139 + -9 Combine like terms: 9.16515139 + -9 = 0.16515139 c = 0.16515139 Simplifying c = 0.16515139Subproblem 2
c + 9 = -9.16515139 Simplifying c + 9 = -9.16515139 Reorder the terms: 9 + c = -9.16515139 Solving 9 + c = -9.16515139 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + c = -9.16515139 + -9 Combine like terms: 9 + -9 = 0 0 + c = -9.16515139 + -9 c = -9.16515139 + -9 Combine like terms: -9.16515139 + -9 = -18.16515139 c = -18.16515139 Simplifying c = -18.16515139Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.16515139, -18.16515139}
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