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Simplifying 2c2 + 8c + -3 = 0 Reorder the terms: -3 + 8c + 2c2 = 0 Solving -3 + 8c + 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'. -1.5 + 4c + c2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 4c + 1.5 + c2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 4c + c2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 4c + c2 = 0 + 1.5 4c + c2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 4c + c2 = 1.5 The c term is 4c. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4c + 4 + c2 = 1.5 + 4 Reorder the terms: 4 + 4c + c2 = 1.5 + 4 Combine like terms: 1.5 + 4 = 5.5 4 + 4c + c2 = 5.5 Factor a perfect square on the left side: (c + 2)(c + 2) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (c + 2) equal to 2.34520788 and -2.34520788.Subproblem 1
c + 2 = 2.34520788 Simplifying c + 2 = 2.34520788 Reorder the terms: 2 + c = 2.34520788 Solving 2 + c = 2.34520788 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = 2.34520788 + -2 Combine like terms: 2 + -2 = 0 0 + c = 2.34520788 + -2 c = 2.34520788 + -2 Combine like terms: 2.34520788 + -2 = 0.34520788 c = 0.34520788 Simplifying c = 0.34520788Subproblem 2
c + 2 = -2.34520788 Simplifying c + 2 = -2.34520788 Reorder the terms: 2 + c = -2.34520788 Solving 2 + c = -2.34520788 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + c = -2.34520788 + -2 Combine like terms: 2 + -2 = 0 0 + c = -2.34520788 + -2 c = -2.34520788 + -2 Combine like terms: -2.34520788 + -2 = -4.34520788 c = -4.34520788 Simplifying c = -4.34520788Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.34520788, -4.34520788}
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