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Simplifying 5c2 + -36c = 33 Reorder the terms: -36c + 5c2 = 33 Solving -36c + 5c2 = 33 Solving for variable 'c'. Reorder the terms: -33 + -36c + 5c2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + -36c + 5c2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.6 + -7.2c + c2 = 0 Move the constant term to the right: Add '6.6' to each side of the equation. -6.6 + -7.2c + 6.6 + c2 = 0 + 6.6 Reorder the terms: -6.6 + 6.6 + -7.2c + c2 = 0 + 6.6 Combine like terms: -6.6 + 6.6 = 0.0 0.0 + -7.2c + c2 = 0 + 6.6 -7.2c + c2 = 0 + 6.6 Combine like terms: 0 + 6.6 = 6.6 -7.2c + c2 = 6.6 The c term is -7.2c. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2c + 12.96 + c2 = 6.6 + 12.96 Reorder the terms: 12.96 + -7.2c + c2 = 6.6 + 12.96 Combine like terms: 6.6 + 12.96 = 19.56 12.96 + -7.2c + c2 = 19.56 Factor a perfect square on the left side: (c + -3.6)(c + -3.6) = 19.56 Calculate the square root of the right side: 4.422668877 Break this problem into two subproblems by setting (c + -3.6) equal to 4.422668877 and -4.422668877.Subproblem 1
c + -3.6 = 4.422668877 Simplifying c + -3.6 = 4.422668877 Reorder the terms: -3.6 + c = 4.422668877 Solving -3.6 + c = 4.422668877 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + c = 4.422668877 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + c = 4.422668877 + 3.6 c = 4.422668877 + 3.6 Combine like terms: 4.422668877 + 3.6 = 8.022668877 c = 8.022668877 Simplifying c = 8.022668877Subproblem 2
c + -3.6 = -4.422668877 Simplifying c + -3.6 = -4.422668877 Reorder the terms: -3.6 + c = -4.422668877 Solving -3.6 + c = -4.422668877 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + c = -4.422668877 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + c = -4.422668877 + 3.6 c = -4.422668877 + 3.6 Combine like terms: -4.422668877 + 3.6 = -0.822668877 c = -0.822668877 Simplifying c = -0.822668877Solution
The solution to the problem is based on the solutions from the subproblems. c = {8.022668877, -0.822668877}
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