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Simplifying 5c2 + -18c + -8c2 + 17 + -10 = 0 Reorder the terms: 17 + -10 + -18c + 5c2 + -8c2 = 0 Combine like terms: 17 + -10 = 7 7 + -18c + 5c2 + -8c2 = 0 Combine like terms: 5c2 + -8c2 = -3c2 7 + -18c + -3c2 = 0 Solving 7 + -18c + -3c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2.333333333 + 6c + c2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 6c + 2.333333333 + c2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 6c + c2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 6c + c2 = 0 + 2.333333333 6c + c2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 6c + c2 = 2.333333333 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 = 2.333333333 + 9 Reorder the terms: 9 + 6c + c2 = 2.333333333 + 9 Combine like terms: 2.333333333 + 9 = 11.333333333 9 + 6c + c2 = 11.333333333 Factor a perfect square on the left side: (c + 3)(c + 3) = 11.333333333 Calculate the square root of the right side: 3.366501646 Break this problem into two subproblems by setting (c + 3) equal to 3.366501646 and -3.366501646.Subproblem 1
c + 3 = 3.366501646 Simplifying c + 3 = 3.366501646 Reorder the terms: 3 + c = 3.366501646 Solving 3 + c = 3.366501646 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 = 3.366501646 + -3 Combine like terms: 3 + -3 = 0 0 + c = 3.366501646 + -3 c = 3.366501646 + -3 Combine like terms: 3.366501646 + -3 = 0.366501646 c = 0.366501646 Simplifying c = 0.366501646Subproblem 2
c + 3 = -3.366501646 Simplifying c + 3 = -3.366501646 Reorder the terms: 3 + c = -3.366501646 Solving 3 + c = -3.366501646 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 = -3.366501646 + -3 Combine like terms: 3 + -3 = 0 0 + c = -3.366501646 + -3 c = -3.366501646 + -3 Combine like terms: -3.366501646 + -3 = -6.366501646 c = -6.366501646 Simplifying c = -6.366501646Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.366501646, -6.366501646}
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