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Simplifying (6c + -4) + -1(c + -3) * c = 7 Reorder the terms: (-4 + 6c) + -1(c + -3) * c = 7 Remove parenthesis around (-4 + 6c) -4 + 6c + -1(c + -3) * c = 7 Reorder the terms: -4 + 6c + -1(-3 + c) * c = 7 Reorder the terms for easier multiplication: -4 + 6c + -1c(-3 + c) = 7 -4 + 6c + (-3 * -1c + c * -1c) = 7 -4 + 6c + (3c + -1c2) = 7 Combine like terms: 6c + 3c = 9c -4 + 9c + -1c2 = 7 Solving -4 + 9c + -1c2 = 7 Solving for variable 'c'. Reorder the terms: -4 + -7 + 9c + -1c2 = 7 + -7 Combine like terms: -4 + -7 = -11 -11 + 9c + -1c2 = 7 + -7 Combine like terms: 7 + -7 = 0 -11 + 9c + -1c2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 11 + -9c + c2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + -9c + -11 + c2 = 0 + -11 Reorder the terms: 11 + -11 + -9c + c2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -9c + c2 = 0 + -11 -9c + c2 = 0 + -11 Combine like terms: 0 + -11 = -11 -9c + c2 = -11 The c term is -9c. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9c + 20.25 + c2 = -11 + 20.25 Reorder the terms: 20.25 + -9c + c2 = -11 + 20.25 Combine like terms: -11 + 20.25 = 9.25 20.25 + -9c + c2 = 9.25 Factor a perfect square on the left side: (c + -4.5)(c + -4.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (c + -4.5) equal to 3.041381265 and -3.041381265.Subproblem 1
c + -4.5 = 3.041381265 Simplifying c + -4.5 = 3.041381265 Reorder the terms: -4.5 + c = 3.041381265 Solving -4.5 + c = 3.041381265 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + c = 3.041381265 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + c = 3.041381265 + 4.5 c = 3.041381265 + 4.5 Combine like terms: 3.041381265 + 4.5 = 7.541381265 c = 7.541381265 Simplifying c = 7.541381265Subproblem 2
c + -4.5 = -3.041381265 Simplifying c + -4.5 = -3.041381265 Reorder the terms: -4.5 + c = -3.041381265 Solving -4.5 + c = -3.041381265 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + c = -3.041381265 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + c = -3.041381265 + 4.5 c = -3.041381265 + 4.5 Combine like terms: -3.041381265 + 4.5 = 1.458618735 c = 1.458618735 Simplifying c = 1.458618735Solution
The solution to the problem is based on the solutions from the subproblems. c = {7.541381265, 1.458618735}
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