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Simplifying 3.5(c + -8) * c = 12.5 Reorder the terms: 3.5(-8 + c) * c = 12.5 Reorder the terms for easier multiplication: 3.5c(-8 + c) = 12.5 (-8 * 3.5c + c * 3.5c) = 12.5 (-28c + 3.5c2) = 12.5 Solving -28c + 3.5c2 = 12.5 Solving for variable 'c'. Reorder the terms: -12.5 + -28c + 3.5c2 = 12.5 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 -12.5 + -28c + 3.5c2 = 0.0 Begin completing the square. Divide all terms by 3.5 the coefficient of the squared term: Divide each side by '3.5'. -3.571428571 + -8c + c2 = 0 Move the constant term to the right: Add '3.571428571' to each side of the equation. -3.571428571 + -8c + 3.571428571 + c2 = 0 + 3.571428571 Reorder the terms: -3.571428571 + 3.571428571 + -8c + c2 = 0 + 3.571428571 Combine like terms: -3.571428571 + 3.571428571 = 0.000000000 0.000000000 + -8c + c2 = 0 + 3.571428571 -8c + c2 = 0 + 3.571428571 Combine like terms: 0 + 3.571428571 = 3.571428571 -8c + c2 = 3.571428571 The c term is -8c. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8c + 16 + c2 = 3.571428571 + 16 Reorder the terms: 16 + -8c + c2 = 3.571428571 + 16 Combine like terms: 3.571428571 + 16 = 19.571428571 16 + -8c + c2 = 19.571428571 Factor a perfect square on the left side: (c + -4)(c + -4) = 19.571428571 Calculate the square root of the right side: 4.423960733 Break this problem into two subproblems by setting (c + -4) equal to 4.423960733 and -4.423960733.Subproblem 1
c + -4 = 4.423960733 Simplifying c + -4 = 4.423960733 Reorder the terms: -4 + c = 4.423960733 Solving -4 + c = 4.423960733 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + c = 4.423960733 + 4 Combine like terms: -4 + 4 = 0 0 + c = 4.423960733 + 4 c = 4.423960733 + 4 Combine like terms: 4.423960733 + 4 = 8.423960733 c = 8.423960733 Simplifying c = 8.423960733Subproblem 2
c + -4 = -4.423960733 Simplifying c + -4 = -4.423960733 Reorder the terms: -4 + c = -4.423960733 Solving -4 + c = -4.423960733 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + c = -4.423960733 + 4 Combine like terms: -4 + 4 = 0 0 + c = -4.423960733 + 4 c = -4.423960733 + 4 Combine like terms: -4.423960733 + 4 = -0.423960733 c = -0.423960733 Simplifying c = -0.423960733Solution
The solution to the problem is based on the solutions from the subproblems. c = {8.423960733, -0.423960733}
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