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Simplifying 3c2 + 7c + -42 = 0 Reorder the terms: -42 + 7c + 3c2 = 0 Solving -42 + 7c + 3c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -14 + 2.333333333c + c2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 2.333333333c + 14 + c2 = 0 + 14 Reorder the terms: -14 + 14 + 2.333333333c + c2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 2.333333333c + c2 = 0 + 14 2.333333333c + c2 = 0 + 14 Combine like terms: 0 + 14 = 14 2.333333333c + c2 = 14 The c term is 2.333333333c. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333c + 1.361111112 + c2 = 14 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333c + c2 = 14 + 1.361111112 Combine like terms: 14 + 1.361111112 = 15.361111112 1.361111112 + 2.333333333c + c2 = 15.361111112 Factor a perfect square on the left side: (c + 1.166666667)(c + 1.166666667) = 15.361111112 Calculate the square root of the right side: 3.919325339 Break this problem into two subproblems by setting (c + 1.166666667) equal to 3.919325339 and -3.919325339.Subproblem 1
c + 1.166666667 = 3.919325339 Simplifying c + 1.166666667 = 3.919325339 Reorder the terms: 1.166666667 + c = 3.919325339 Solving 1.166666667 + c = 3.919325339 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + c = 3.919325339 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + c = 3.919325339 + -1.166666667 c = 3.919325339 + -1.166666667 Combine like terms: 3.919325339 + -1.166666667 = 2.752658672 c = 2.752658672 Simplifying c = 2.752658672Subproblem 2
c + 1.166666667 = -3.919325339 Simplifying c + 1.166666667 = -3.919325339 Reorder the terms: 1.166666667 + c = -3.919325339 Solving 1.166666667 + c = -3.919325339 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + c = -3.919325339 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + c = -3.919325339 + -1.166666667 c = -3.919325339 + -1.166666667 Combine like terms: -3.919325339 + -1.166666667 = -5.085992006 c = -5.085992006 Simplifying c = -5.085992006Solution
The solution to the problem is based on the solutions from the subproblems. c = {2.752658672, -5.085992006}
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