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Simplifying (6c2 + -5) + -1(4c2 + 9c + 5) = 0 Reorder the terms: (-5 + 6c2) + -1(4c2 + 9c + 5) = 0 Remove parenthesis around (-5 + 6c2) -5 + 6c2 + -1(4c2 + 9c + 5) = 0 Reorder the terms: -5 + 6c2 + -1(5 + 9c + 4c2) = 0 -5 + 6c2 + (5 * -1 + 9c * -1 + 4c2 * -1) = 0 -5 + 6c2 + (-5 + -9c + -4c2) = 0 Reorder the terms: -5 + -5 + -9c + 6c2 + -4c2 = 0 Combine like terms: -5 + -5 = -10 -10 + -9c + 6c2 + -4c2 = 0 Combine like terms: 6c2 + -4c2 = 2c2 -10 + -9c + 2c2 = 0 Solving -10 + -9c + 2c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + -4.5c + c2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -4.5c + 5 + c2 = 0 + 5 Reorder the terms: -5 + 5 + -4.5c + c2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4.5c + c2 = 0 + 5 -4.5c + c2 = 0 + 5 Combine like terms: 0 + 5 = 5 -4.5c + c2 = 5 The c term is -4.5c. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5c + 5.0625 + c2 = 5 + 5.0625 Reorder the terms: 5.0625 + -4.5c + c2 = 5 + 5.0625 Combine like terms: 5 + 5.0625 = 10.0625 5.0625 + -4.5c + c2 = 10.0625 Factor a perfect square on the left side: (c + -2.25)(c + -2.25) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (c + -2.25) equal to 3.172144385 and -3.172144385.Subproblem 1
c + -2.25 = 3.172144385 Simplifying c + -2.25 = 3.172144385 Reorder the terms: -2.25 + c = 3.172144385 Solving -2.25 + c = 3.172144385 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + c = 3.172144385 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + c = 3.172144385 + 2.25 c = 3.172144385 + 2.25 Combine like terms: 3.172144385 + 2.25 = 5.422144385 c = 5.422144385 Simplifying c = 5.422144385Subproblem 2
c + -2.25 = -3.172144385 Simplifying c + -2.25 = -3.172144385 Reorder the terms: -2.25 + c = -3.172144385 Solving -2.25 + c = -3.172144385 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + c = -3.172144385 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + c = -3.172144385 + 2.25 c = -3.172144385 + 2.25 Combine like terms: -3.172144385 + 2.25 = -0.922144385 c = -0.922144385 Simplifying c = -0.922144385Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.422144385, -0.922144385}
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