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Simplifying 0 = 2c2 + -10c + -8 Reorder the terms: 0 = -8 + -10c + 2c2 Solving 0 = -8 + -10c + 2c2 Solving for variable 'c'. Combine like terms: 0 + 8 = 8 8 + 10c + -2c2 = -8 + -10c + 2c2 + 8 + 10c + -2c2 Reorder the terms: 8 + 10c + -2c2 = -8 + 8 + -10c + 10c + 2c2 + -2c2 Combine like terms: -8 + 8 = 0 8 + 10c + -2c2 = 0 + -10c + 10c + 2c2 + -2c2 8 + 10c + -2c2 = -10c + 10c + 2c2 + -2c2 Combine like terms: -10c + 10c = 0 8 + 10c + -2c2 = 0 + 2c2 + -2c2 8 + 10c + -2c2 = 2c2 + -2c2 Combine like terms: 2c2 + -2c2 = 0 8 + 10c + -2c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 5c + -1c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 5c + -1c2)' equal to zero and attempt to solve: Simplifying 4 + 5c + -1c2 = 0 Solving 4 + 5c + -1c2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -5c + c2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -5c + 4 + c2 = 0 + 4 Reorder the terms: -4 + 4 + -5c + c2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5c + c2 = 0 + 4 -5c + c2 = 0 + 4 Combine like terms: 0 + 4 = 4 -5c + c2 = 4 The c term is -5c. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5c + 6.25 + c2 = 4 + 6.25 Reorder the terms: 6.25 + -5c + c2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + -5c + c2 = 10.25 Factor a perfect square on the left side: (c + -2.5)(c + -2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (c + -2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
c + -2.5 = 3.201562119 Simplifying c + -2.5 = 3.201562119 Reorder the terms: -2.5 + c = 3.201562119 Solving -2.5 + c = 3.201562119 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + c = 3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + c = 3.201562119 + 2.5 c = 3.201562119 + 2.5 Combine like terms: 3.201562119 + 2.5 = 5.701562119 c = 5.701562119 Simplifying c = 5.701562119Subproblem 2
c + -2.5 = -3.201562119 Simplifying c + -2.5 = -3.201562119 Reorder the terms: -2.5 + c = -3.201562119 Solving -2.5 + c = -3.201562119 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + c = -3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + c = -3.201562119 + 2.5 c = -3.201562119 + 2.5 Combine like terms: -3.201562119 + 2.5 = -0.701562119 c = -0.701562119 Simplifying c = -0.701562119Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.701562119, -0.701562119}Solution
c = {5.701562119, -0.701562119}
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