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Simplifying 4(C + -9) * C = 15 Reorder the terms: 4(-9 + C) * C = 15 Reorder the terms for easier multiplication: 4C(-9 + C) = 15 (-9 * 4C + C * 4C) = 15 (-36C + 4C2) = 15 Solving -36C + 4C2 = 15 Solving for variable 'C'. Reorder the terms: -15 + -36C + 4C2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -36C + 4C2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -9C + C2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -9C + 3.75 + C2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -9C + C2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -9C + C2 = 0 + 3.75 -9C + C2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -9C + C2 = 3.75 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 = 3.75 + 20.25 Reorder the terms: 20.25 + -9C + C2 = 3.75 + 20.25 Combine like terms: 3.75 + 20.25 = 24 20.25 + -9C + C2 = 24 Factor a perfect square on the left side: (C + -4.5)(C + -4.5) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (C + -4.5) equal to 4.898979486 and -4.898979486.Subproblem 1
C + -4.5 = 4.898979486 Simplifying C + -4.5 = 4.898979486 Reorder the terms: -4.5 + C = 4.898979486 Solving -4.5 + C = 4.898979486 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 = 4.898979486 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + C = 4.898979486 + 4.5 C = 4.898979486 + 4.5 Combine like terms: 4.898979486 + 4.5 = 9.398979486 C = 9.398979486 Simplifying C = 9.398979486Subproblem 2
C + -4.5 = -4.898979486 Simplifying C + -4.5 = -4.898979486 Reorder the terms: -4.5 + C = -4.898979486 Solving -4.5 + C = -4.898979486 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 = -4.898979486 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + C = -4.898979486 + 4.5 C = -4.898979486 + 4.5 Combine like terms: -4.898979486 + 4.5 = -0.398979486 C = -0.398979486 Simplifying C = -0.398979486Solution
The solution to the problem is based on the solutions from the subproblems. C = {9.398979486, -0.398979486}
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