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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 = 3 3 + 9c + -1c2 = -7 + 7 Combine like terms: -7 + 7 = 0 3 + 9c + -1c2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -9c + c2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -9c + 3 + c2 = 0 + 3 Reorder the terms: -3 + 3 + -9c + c2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -9c + c2 = 0 + 3 -9c + c2 = 0 + 3 Combine like terms: 0 + 3 = 3 -9c + c2 = 3 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 = 3 + 20.25 Reorder the terms: 20.25 + -9c + c2 = 3 + 20.25 Combine like terms: 3 + 20.25 = 23.25 20.25 + -9c + c2 = 23.25 Factor a perfect square on the left side: (c + -4.5)(c + -4.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (c + -4.5) equal to 4.82182538 and -4.82182538.Subproblem 1
c + -4.5 = 4.82182538 Simplifying c + -4.5 = 4.82182538 Reorder the terms: -4.5 + c = 4.82182538 Solving -4.5 + c = 4.82182538 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 = 4.82182538 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + c = 4.82182538 + 4.5 c = 4.82182538 + 4.5 Combine like terms: 4.82182538 + 4.5 = 9.32182538 c = 9.32182538 Simplifying c = 9.32182538Subproblem 2
c + -4.5 = -4.82182538 Simplifying c + -4.5 = -4.82182538 Reorder the terms: -4.5 + c = -4.82182538 Solving -4.5 + c = -4.82182538 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 = -4.82182538 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + c = -4.82182538 + 4.5 c = -4.82182538 + 4.5 Combine like terms: -4.82182538 + 4.5 = -0.32182538 c = -0.32182538 Simplifying c = -0.32182538Solution
The solution to the problem is based on the solutions from the subproblems. c = {9.32182538, -0.32182538}
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