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Simplifying 2c2 + 3c + -13 = -3c2 Reorder the terms: -13 + 3c + 2c2 = -3c2 Solving -13 + 3c + 2c2 = -3c2 Solving for variable 'c'. Combine like terms: 2c2 + 3c2 = 5c2 -13 + 3c + 5c2 = -3c2 + 3c2 Combine like terms: -3c2 + 3c2 = 0 -13 + 3c + 5c2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + 0.6c + c2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 0.6c + 2.6 + c2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + 0.6c + c2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 0.6c + c2 = 0 + 2.6 0.6c + c2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 0.6c + c2 = 2.6 The c term is 0.6c. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6c + 0.09 + c2 = 2.6 + 0.09 Reorder the terms: 0.09 + 0.6c + c2 = 2.6 + 0.09 Combine like terms: 2.6 + 0.09 = 2.69 0.09 + 0.6c + c2 = 2.69 Factor a perfect square on the left side: (c + 0.3)(c + 0.3) = 2.69 Calculate the square root of the right side: 1.640121947 Break this problem into two subproblems by setting (c + 0.3) equal to 1.640121947 and -1.640121947.Subproblem 1
c + 0.3 = 1.640121947 Simplifying c + 0.3 = 1.640121947 Reorder the terms: 0.3 + c = 1.640121947 Solving 0.3 + c = 1.640121947 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + c = 1.640121947 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + c = 1.640121947 + -0.3 c = 1.640121947 + -0.3 Combine like terms: 1.640121947 + -0.3 = 1.340121947 c = 1.340121947 Simplifying c = 1.340121947Subproblem 2
c + 0.3 = -1.640121947 Simplifying c + 0.3 = -1.640121947 Reorder the terms: 0.3 + c = -1.640121947 Solving 0.3 + c = -1.640121947 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + c = -1.640121947 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + c = -1.640121947 + -0.3 c = -1.640121947 + -0.3 Combine like terms: -1.640121947 + -0.3 = -1.940121947 c = -1.940121947 Simplifying c = -1.940121947Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.340121947, -1.940121947}
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