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Simplifying 2c2 + -9c + -15 = 0 Reorder the terms: -15 + -9c + 2c2 = 0 Solving -15 + -9c + 2c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + -4.5c + c2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -4.5c + 7.5 + c2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -4.5c + c2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -4.5c + c2 = 0 + 7.5 -4.5c + c2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -4.5c + c2 = 7.5 The c term is -4.5c. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5c + 5.0625 + c2 = 7.5 + 5.0625 Reorder the terms: 5.0625 + -4.5c + c2 = 7.5 + 5.0625 Combine like terms: 7.5 + 5.0625 = 12.5625 5.0625 + -4.5c + c2 = 12.5625 Factor a perfect square on the left side: (c + -2.25)(c + -2.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (c + -2.25) equal to 3.54436172 and -3.54436172.Subproblem 1
c + -2.25 = 3.54436172 Simplifying c + -2.25 = 3.54436172 Reorder the terms: -2.25 + c = 3.54436172 Solving -2.25 + c = 3.54436172 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + c = 3.54436172 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + c = 3.54436172 + 2.25 c = 3.54436172 + 2.25 Combine like terms: 3.54436172 + 2.25 = 5.79436172 c = 5.79436172 Simplifying c = 5.79436172Subproblem 2
c + -2.25 = -3.54436172 Simplifying c + -2.25 = -3.54436172 Reorder the terms: -2.25 + c = -3.54436172 Solving -2.25 + c = -3.54436172 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + c = -3.54436172 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + c = -3.54436172 + 2.25 c = -3.54436172 + 2.25 Combine like terms: -3.54436172 + 2.25 = -1.29436172 c = -1.29436172 Simplifying c = -1.29436172Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.79436172, -1.29436172}
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