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Simplifying 2c2 + -7c = 19 Reorder the terms: -7c + 2c2 = 19 Solving -7c + 2c2 = 19 Solving for variable 'c'. Reorder the terms: -19 + -7c + 2c2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + -7c + 2c2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + -3.5c + c2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + -3.5c + 9.5 + c2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + -3.5c + c2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + -3.5c + c2 = 0 + 9.5 -3.5c + c2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 -3.5c + c2 = 9.5 The c term is -3.5c. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5c + 3.0625 + c2 = 9.5 + 3.0625 Reorder the terms: 3.0625 + -3.5c + c2 = 9.5 + 3.0625 Combine like terms: 9.5 + 3.0625 = 12.5625 3.0625 + -3.5c + c2 = 12.5625 Factor a perfect square on the left side: (c + -1.75)(c + -1.75) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (c + -1.75) equal to 3.54436172 and -3.54436172.Subproblem 1
c + -1.75 = 3.54436172 Simplifying c + -1.75 = 3.54436172 Reorder the terms: -1.75 + c = 3.54436172 Solving -1.75 + c = 3.54436172 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + c = 3.54436172 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + c = 3.54436172 + 1.75 c = 3.54436172 + 1.75 Combine like terms: 3.54436172 + 1.75 = 5.29436172 c = 5.29436172 Simplifying c = 5.29436172Subproblem 2
c + -1.75 = -3.54436172 Simplifying c + -1.75 = -3.54436172 Reorder the terms: -1.75 + c = -3.54436172 Solving -1.75 + c = -3.54436172 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + c = -3.54436172 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + c = -3.54436172 + 1.75 c = -3.54436172 + 1.75 Combine like terms: -3.54436172 + 1.75 = -1.79436172 c = -1.79436172 Simplifying c = -1.79436172Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.29436172, -1.79436172}
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