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Simplifying 7c2 + -19c + -10 = 0 Reorder the terms: -10 + -19c + 7c2 = 0 Solving -10 + -19c + 7c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + -2.714285714c + c2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -2.714285714c + 1.428571429 + c2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -2.714285714c + c2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -2.714285714c + c2 = 0 + 1.428571429 -2.714285714c + c2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -2.714285714c + c2 = 1.428571429 The c term is -2.714285714c. Take half its coefficient (-1.357142857). Square it (1.841836734) and add it to both sides. Add '1.841836734' to each side of the equation. -2.714285714c + 1.841836734 + c2 = 1.428571429 + 1.841836734 Reorder the terms: 1.841836734 + -2.714285714c + c2 = 1.428571429 + 1.841836734 Combine like terms: 1.428571429 + 1.841836734 = 3.270408163 1.841836734 + -2.714285714c + c2 = 3.270408163 Factor a perfect square on the left side: (c + -1.357142857)(c + -1.357142857) = 3.270408163 Calculate the square root of the right side: 1.808426986 Break this problem into two subproblems by setting (c + -1.357142857) equal to 1.808426986 and -1.808426986.Subproblem 1
c + -1.357142857 = 1.808426986 Simplifying c + -1.357142857 = 1.808426986 Reorder the terms: -1.357142857 + c = 1.808426986 Solving -1.357142857 + c = 1.808426986 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + c = 1.808426986 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + c = 1.808426986 + 1.357142857 c = 1.808426986 + 1.357142857 Combine like terms: 1.808426986 + 1.357142857 = 3.165569843 c = 3.165569843 Simplifying c = 3.165569843Subproblem 2
c + -1.357142857 = -1.808426986 Simplifying c + -1.357142857 = -1.808426986 Reorder the terms: -1.357142857 + c = -1.808426986 Solving -1.357142857 + c = -1.808426986 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + c = -1.808426986 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + c = -1.808426986 + 1.357142857 c = -1.808426986 + 1.357142857 Combine like terms: -1.808426986 + 1.357142857 = -0.451284129 c = -0.451284129 Simplifying c = -0.451284129Solution
The solution to the problem is based on the solutions from the subproblems. c = {3.165569843, -0.451284129}
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