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Simplifying 3c + 4 = 2c(c + -5) Reorder the terms: 4 + 3c = 2c(c + -5) Reorder the terms: 4 + 3c = 2c(-5 + c) 4 + 3c = (-5 * 2c + c * 2c) 4 + 3c = (-10c + 2c2) Solving 4 + 3c = -10c + 2c2 Solving for variable 'c'. Combine like terms: 3c + 10c = 13c 4 + 13c + -2c2 = -10c + 2c2 + 10c + -2c2 Reorder the terms: 4 + 13c + -2c2 = -10c + 10c + 2c2 + -2c2 Combine like terms: -10c + 10c = 0 4 + 13c + -2c2 = 0 + 2c2 + -2c2 4 + 13c + -2c2 = 2c2 + -2c2 Combine like terms: 2c2 + -2c2 = 0 4 + 13c + -2c2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -2 + -6.5c + c2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -6.5c + 2 + c2 = 0 + 2 Reorder the terms: -2 + 2 + -6.5c + c2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -6.5c + c2 = 0 + 2 -6.5c + c2 = 0 + 2 Combine like terms: 0 + 2 = 2 -6.5c + c2 = 2 The c term is -6.5c. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5c + 10.5625 + c2 = 2 + 10.5625 Reorder the terms: 10.5625 + -6.5c + c2 = 2 + 10.5625 Combine like terms: 2 + 10.5625 = 12.5625 10.5625 + -6.5c + c2 = 12.5625 Factor a perfect square on the left side: (c + -3.25)(c + -3.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (c + -3.25) equal to 3.54436172 and -3.54436172.Subproblem 1
c + -3.25 = 3.54436172 Simplifying c + -3.25 = 3.54436172 Reorder the terms: -3.25 + c = 3.54436172 Solving -3.25 + c = 3.54436172 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + c = 3.54436172 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + c = 3.54436172 + 3.25 c = 3.54436172 + 3.25 Combine like terms: 3.54436172 + 3.25 = 6.79436172 c = 6.79436172 Simplifying c = 6.79436172Subproblem 2
c + -3.25 = -3.54436172 Simplifying c + -3.25 = -3.54436172 Reorder the terms: -3.25 + c = -3.54436172 Solving -3.25 + c = -3.54436172 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + c = -3.54436172 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + c = -3.54436172 + 3.25 c = -3.54436172 + 3.25 Combine like terms: -3.54436172 + 3.25 = -0.29436172 c = -0.29436172 Simplifying c = -0.29436172Solution
The solution to the problem is based on the solutions from the subproblems. c = {6.79436172, -0.29436172}
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