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Simplifying 6(c + -4) * c = 7 Reorder the terms: 6(-4 + c) * c = 7 Reorder the terms for easier multiplication: 6c(-4 + c) = 7 (-4 * 6c + c * 6c) = 7 (-24c + 6c2) = 7 Solving -24c + 6c2 = 7 Solving for variable 'c'. Reorder the terms: -7 + -24c + 6c2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -24c + 6c2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.166666667 + -4c + c2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + -4c + 1.166666667 + c2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + -4c + c2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + -4c + c2 = 0 + 1.166666667 -4c + c2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 -4c + c2 = 1.166666667 The c term is -4c. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4c + 4 + c2 = 1.166666667 + 4 Reorder the terms: 4 + -4c + c2 = 1.166666667 + 4 Combine like terms: 1.166666667 + 4 = 5.166666667 4 + -4c + c2 = 5.166666667 Factor a perfect square on the left side: (c + -2)(c + -2) = 5.166666667 Calculate the square root of the right side: 2.273030283 Break this problem into two subproblems by setting (c + -2) equal to 2.273030283 and -2.273030283.Subproblem 1
c + -2 = 2.273030283 Simplifying c + -2 = 2.273030283 Reorder the terms: -2 + c = 2.273030283 Solving -2 + c = 2.273030283 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c = 2.273030283 + 2 Combine like terms: -2 + 2 = 0 0 + c = 2.273030283 + 2 c = 2.273030283 + 2 Combine like terms: 2.273030283 + 2 = 4.273030283 c = 4.273030283 Simplifying c = 4.273030283Subproblem 2
c + -2 = -2.273030283 Simplifying c + -2 = -2.273030283 Reorder the terms: -2 + c = -2.273030283 Solving -2 + c = -2.273030283 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c = -2.273030283 + 2 Combine like terms: -2 + 2 = 0 0 + c = -2.273030283 + 2 c = -2.273030283 + 2 Combine like terms: -2.273030283 + 2 = -0.273030283 c = -0.273030283 Simplifying c = -0.273030283Solution
The solution to the problem is based on the solutions from the subproblems. c = {4.273030283, -0.273030283}
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