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Simplifying 4c2 + 21c + 15 = 0 Reorder the terms: 15 + 21c + 4c2 = 0 Solving 15 + 21c + 4c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + 5.25c + c2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 5.25c + -3.75 + c2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 5.25c + c2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 5.25c + c2 = 0 + -3.75 5.25c + c2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 5.25c + c2 = -3.75 The c term is 5.25c. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25c + 6.890625 + c2 = -3.75 + 6.890625 Reorder the terms: 6.890625 + 5.25c + c2 = -3.75 + 6.890625 Combine like terms: -3.75 + 6.890625 = 3.140625 6.890625 + 5.25c + c2 = 3.140625 Factor a perfect square on the left side: (c + 2.625)(c + 2.625) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (c + 2.625) equal to 1.77218086 and -1.77218086.Subproblem 1
c + 2.625 = 1.77218086 Simplifying c + 2.625 = 1.77218086 Reorder the terms: 2.625 + c = 1.77218086 Solving 2.625 + c = 1.77218086 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + c = 1.77218086 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + c = 1.77218086 + -2.625 c = 1.77218086 + -2.625 Combine like terms: 1.77218086 + -2.625 = -0.85281914 c = -0.85281914 Simplifying c = -0.85281914Subproblem 2
c + 2.625 = -1.77218086 Simplifying c + 2.625 = -1.77218086 Reorder the terms: 2.625 + c = -1.77218086 Solving 2.625 + c = -1.77218086 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + c = -1.77218086 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + c = -1.77218086 + -2.625 c = -1.77218086 + -2.625 Combine like terms: -1.77218086 + -2.625 = -4.39718086 c = -4.39718086 Simplifying c = -4.39718086Solution
The solution to the problem is based on the solutions from the subproblems. c = {-0.85281914, -4.39718086}
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