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Simplifying 3 + 2c + -2c2 = 0 Solving 3 + 2c + -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 + -1c + c2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -1c + 1.5 + c2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -1c + c2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -1c + c2 = 0 + 1.5 -1c + c2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -1c + c2 = 1.5 The c term is -1c. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1c + 0.25 + c2 = 1.5 + 0.25 Reorder the terms: 0.25 + -1c + c2 = 1.5 + 0.25 Combine like terms: 1.5 + 0.25 = 1.75 0.25 + -1c + c2 = 1.75 Factor a perfect square on the left side: (c + -0.5)(c + -0.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (c + -0.5) equal to 1.322875656 and -1.322875656.Subproblem 1
c + -0.5 = 1.322875656 Simplifying c + -0.5 = 1.322875656 Reorder the terms: -0.5 + c = 1.322875656 Solving -0.5 + c = 1.322875656 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + c = 1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = 1.322875656 + 0.5 c = 1.322875656 + 0.5 Combine like terms: 1.322875656 + 0.5 = 1.822875656 c = 1.822875656 Simplifying c = 1.822875656Subproblem 2
c + -0.5 = -1.322875656 Simplifying c + -0.5 = -1.322875656 Reorder the terms: -0.5 + c = -1.322875656 Solving -0.5 + c = -1.322875656 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + c = -1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + c = -1.322875656 + 0.5 c = -1.322875656 + 0.5 Combine like terms: -1.322875656 + 0.5 = -0.822875656 c = -0.822875656 Simplifying c = -0.822875656Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.822875656, -0.822875656}
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