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Simplifying 49c2 + -4c + -13 = 0 Reorder the terms: -13 + -4c + 49c2 = 0 Solving -13 + -4c + 49c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.2653061224 + -0.08163265306c + c2 = 0 Move the constant term to the right: Add '0.2653061224' to each side of the equation. -0.2653061224 + -0.08163265306c + 0.2653061224 + c2 = 0 + 0.2653061224 Reorder the terms: -0.2653061224 + 0.2653061224 + -0.08163265306c + c2 = 0 + 0.2653061224 Combine like terms: -0.2653061224 + 0.2653061224 = 0.0000000000 0.0000000000 + -0.08163265306c + c2 = 0 + 0.2653061224 -0.08163265306c + c2 = 0 + 0.2653061224 Combine like terms: 0 + 0.2653061224 = 0.2653061224 -0.08163265306c + c2 = 0.2653061224 The c term is -0.08163265306c. Take half its coefficient (-0.04081632653). Square it (0.001665972511) and add it to both sides. Add '0.001665972511' to each side of the equation. -0.08163265306c + 0.001665972511 + c2 = 0.2653061224 + 0.001665972511 Reorder the terms: 0.001665972511 + -0.08163265306c + c2 = 0.2653061224 + 0.001665972511 Combine like terms: 0.2653061224 + 0.001665972511 = 0.266972094911 0.001665972511 + -0.08163265306c + c2 = 0.266972094911 Factor a perfect square on the left side: (c + -0.04081632653)(c + -0.04081632653) = 0.266972094911 Calculate the square root of the right side: 0.516693424 Break this problem into two subproblems by setting (c + -0.04081632653) equal to 0.516693424 and -0.516693424.Subproblem 1
c + -0.04081632653 = 0.516693424 Simplifying c + -0.04081632653 = 0.516693424 Reorder the terms: -0.04081632653 + c = 0.516693424 Solving -0.04081632653 + c = 0.516693424 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.04081632653' to each side of the equation. -0.04081632653 + 0.04081632653 + c = 0.516693424 + 0.04081632653 Combine like terms: -0.04081632653 + 0.04081632653 = 0.00000000000 0.00000000000 + c = 0.516693424 + 0.04081632653 c = 0.516693424 + 0.04081632653 Combine like terms: 0.516693424 + 0.04081632653 = 0.55750975053 c = 0.55750975053 Simplifying c = 0.55750975053Subproblem 2
c + -0.04081632653 = -0.516693424 Simplifying c + -0.04081632653 = -0.516693424 Reorder the terms: -0.04081632653 + c = -0.516693424 Solving -0.04081632653 + c = -0.516693424 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.04081632653' to each side of the equation. -0.04081632653 + 0.04081632653 + c = -0.516693424 + 0.04081632653 Combine like terms: -0.04081632653 + 0.04081632653 = 0.00000000000 0.00000000000 + c = -0.516693424 + 0.04081632653 c = -0.516693424 + 0.04081632653 Combine like terms: -0.516693424 + 0.04081632653 = -0.47587709747 c = -0.47587709747 Simplifying c = -0.47587709747Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.55750975053, -0.47587709747}
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