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Simplifying c2 + 14c + -3 = 0 Reorder the terms: -3 + 14c + c2 = 0 Solving -3 + 14c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 14c + 3 + c2 = 0 + 3 Reorder the terms: -3 + 3 + 14c + c2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 14c + c2 = 0 + 3 14c + c2 = 0 + 3 Combine like terms: 0 + 3 = 3 14c + c2 = 3 The c term is 14c. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14c + 49 + c2 = 3 + 49 Reorder the terms: 49 + 14c + c2 = 3 + 49 Combine like terms: 3 + 49 = 52 49 + 14c + c2 = 52 Factor a perfect square on the left side: (c + 7)(c + 7) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (c + 7) equal to 7.211102551 and -7.211102551.Subproblem 1
c + 7 = 7.211102551 Simplifying c + 7 = 7.211102551 Reorder the terms: 7 + c = 7.211102551 Solving 7 + c = 7.211102551 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + c = 7.211102551 + -7 Combine like terms: 7 + -7 = 0 0 + c = 7.211102551 + -7 c = 7.211102551 + -7 Combine like terms: 7.211102551 + -7 = 0.211102551 c = 0.211102551 Simplifying c = 0.211102551Subproblem 2
c + 7 = -7.211102551 Simplifying c + 7 = -7.211102551 Reorder the terms: 7 + c = -7.211102551 Solving 7 + c = -7.211102551 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + c = -7.211102551 + -7 Combine like terms: 7 + -7 = 0 0 + c = -7.211102551 + -7 c = -7.211102551 + -7 Combine like terms: -7.211102551 + -7 = -14.211102551 c = -14.211102551 Simplifying c = -14.211102551Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.211102551, -14.211102551}
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