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Simplifying 4c2 + 4c + -14 = 0 Reorder the terms: -14 + 4c + 4c2 = 0 Solving -14 + 4c + 4c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 2c + 2c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 2c + 2c2)' equal to zero and attempt to solve: Simplifying -7 + 2c + 2c2 = 0 Solving -7 + 2c + 2c2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + c + c2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + c + 3.5 + c2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + c + c2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + c + c2 = 0 + 3.5 c + c2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 c + c2 = 3.5 The c term is c. 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. + 0.25 + c2 = 3.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + c2 = 3.5 + 0.25 Combine like terms: 3.5 + 0.25 = 3.75 1.25 + c2 = 3.75 Factor a perfect square on the left side: (c + 0.5)(c + 0.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (c + 0.5) equal to 1.936491673 and -1.936491673.Subproblem 1
c + 0.5 = 1.936491673 Simplifying c + 0.5 = 1.936491673 Reorder the terms: 0.5 + c = 1.936491673 Solving 0.5 + c = 1.936491673 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 = 1.936491673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = 1.936491673 + -0.5 c = 1.936491673 + -0.5 Combine like terms: 1.936491673 + -0.5 = 1.436491673 c = 1.436491673 Simplifying c = 1.436491673Subproblem 2
c + 0.5 = -1.936491673 Simplifying c + 0.5 = -1.936491673 Reorder the terms: 0.5 + c = -1.936491673 Solving 0.5 + c = -1.936491673 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 = -1.936491673 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = -1.936491673 + -0.5 c = -1.936491673 + -0.5 Combine like terms: -1.936491673 + -0.5 = -2.436491673 c = -2.436491673 Simplifying c = -2.436491673Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.436491673, -2.436491673}Solution
c = {1.436491673, -2.436491673}
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