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Simplifying 4c2 + -25c = 22 Reorder the terms: -25c + 4c2 = 22 Solving -25c + 4c2 = 22 Solving for variable 'c'. Reorder the terms: -22 + -25c + 4c2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + -25c + 4c2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.5 + -6.25c + c2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -6.25c + 5.5 + c2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -6.25c + c2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -6.25c + c2 = 0 + 5.5 -6.25c + c2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -6.25c + c2 = 5.5 The c term is -6.25c. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25c + 9.765625 + c2 = 5.5 + 9.765625 Reorder the terms: 9.765625 + -6.25c + c2 = 5.5 + 9.765625 Combine like terms: 5.5 + 9.765625 = 15.265625 9.765625 + -6.25c + c2 = 15.265625 Factor a perfect square on the left side: (c + -3.125)(c + -3.125) = 15.265625 Calculate the square root of the right side: 3.907124902 Break this problem into two subproblems by setting (c + -3.125) equal to 3.907124902 and -3.907124902.Subproblem 1
c + -3.125 = 3.907124902 Simplifying c + -3.125 = 3.907124902 Reorder the terms: -3.125 + c = 3.907124902 Solving -3.125 + c = 3.907124902 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + c = 3.907124902 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + c = 3.907124902 + 3.125 c = 3.907124902 + 3.125 Combine like terms: 3.907124902 + 3.125 = 7.032124902 c = 7.032124902 Simplifying c = 7.032124902Subproblem 2
c + -3.125 = -3.907124902 Simplifying c + -3.125 = -3.907124902 Reorder the terms: -3.125 + c = -3.907124902 Solving -3.125 + c = -3.907124902 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + c = -3.907124902 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + c = -3.907124902 + 3.125 c = -3.907124902 + 3.125 Combine like terms: -3.907124902 + 3.125 = -0.782124902 c = -0.782124902 Simplifying c = -0.782124902Solution
The solution to the problem is based on the solutions from the subproblems. c = {7.032124902, -0.782124902}
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