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Simplifying 10c2 + 4c + -27 = 0 Reorder the terms: -27 + 4c + 10c2 = 0 Solving -27 + 4c + 10c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.7 + 0.4c + c2 = 0 Move the constant term to the right: Add '2.7' to each side of the equation. -2.7 + 0.4c + 2.7 + c2 = 0 + 2.7 Reorder the terms: -2.7 + 2.7 + 0.4c + c2 = 0 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + 0.4c + c2 = 0 + 2.7 0.4c + c2 = 0 + 2.7 Combine like terms: 0 + 2.7 = 2.7 0.4c + c2 = 2.7 The c term is 0.4c. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4c + 0.04 + c2 = 2.7 + 0.04 Reorder the terms: 0.04 + 0.4c + c2 = 2.7 + 0.04 Combine like terms: 2.7 + 0.04 = 2.74 0.04 + 0.4c + c2 = 2.74 Factor a perfect square on the left side: (c + 0.2)(c + 0.2) = 2.74 Calculate the square root of the right side: 1.655294536 Break this problem into two subproblems by setting (c + 0.2) equal to 1.655294536 and -1.655294536.Subproblem 1
c + 0.2 = 1.655294536 Simplifying c + 0.2 = 1.655294536 Reorder the terms: 0.2 + c = 1.655294536 Solving 0.2 + c = 1.655294536 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + c = 1.655294536 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + c = 1.655294536 + -0.2 c = 1.655294536 + -0.2 Combine like terms: 1.655294536 + -0.2 = 1.455294536 c = 1.455294536 Simplifying c = 1.455294536Subproblem 2
c + 0.2 = -1.655294536 Simplifying c + 0.2 = -1.655294536 Reorder the terms: 0.2 + c = -1.655294536 Solving 0.2 + c = -1.655294536 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + c = -1.655294536 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + c = -1.655294536 + -0.2 c = -1.655294536 + -0.2 Combine like terms: -1.655294536 + -0.2 = -1.855294536 c = -1.855294536 Simplifying c = -1.855294536Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.455294536, -1.855294536}
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