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Simplifying 10c + 3c(c + -7) = 18 Reorder the terms: 10c + 3c(-7 + c) = 18 10c + (-7 * 3c + c * 3c) = 18 10c + (-21c + 3c2) = 18 Combine like terms: 10c + -21c = -11c -11c + 3c2 = 18 Solving -11c + 3c2 = 18 Solving for variable 'c'. Reorder the terms: -18 + -11c + 3c2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -11c + 3c2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + -3.666666667c + c2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -3.666666667c + 6 + c2 = 0 + 6 Reorder the terms: -6 + 6 + -3.666666667c + c2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -3.666666667c + c2 = 0 + 6 -3.666666667c + c2 = 0 + 6 Combine like terms: 0 + 6 = 6 -3.666666667c + c2 = 6 The c term is -3.666666667c. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667c + 3.361111114 + c2 = 6 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667c + c2 = 6 + 3.361111114 Combine like terms: 6 + 3.361111114 = 9.361111114 3.361111114 + -3.666666667c + c2 = 9.361111114 Factor a perfect square on the left side: (c + -1.833333334)(c + -1.833333334) = 9.361111114 Calculate the square root of the right side: 3.059593292 Break this problem into two subproblems by setting (c + -1.833333334) equal to 3.059593292 and -3.059593292.Subproblem 1
c + -1.833333334 = 3.059593292 Simplifying c + -1.833333334 = 3.059593292 Reorder the terms: -1.833333334 + c = 3.059593292 Solving -1.833333334 + c = 3.059593292 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + c = 3.059593292 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + c = 3.059593292 + 1.833333334 c = 3.059593292 + 1.833333334 Combine like terms: 3.059593292 + 1.833333334 = 4.892926626 c = 4.892926626 Simplifying c = 4.892926626Subproblem 2
c + -1.833333334 = -3.059593292 Simplifying c + -1.833333334 = -3.059593292 Reorder the terms: -1.833333334 + c = -3.059593292 Solving -1.833333334 + c = -3.059593292 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + c = -3.059593292 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + c = -3.059593292 + 1.833333334 c = -3.059593292 + 1.833333334 Combine like terms: -3.059593292 + 1.833333334 = -1.226259958 c = -1.226259958 Simplifying c = -1.226259958Solution
The solution to the problem is based on the solutions from the subproblems. c = {4.892926626, -1.226259958}
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