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Simplifying 3c2 + -1c + -18 = 5c2 + -5c + -36 Reorder the terms: -18 + -1c + 3c2 = 5c2 + -5c + -36 Reorder the terms: -18 + -1c + 3c2 = -36 + -5c + 5c2 Solving -18 + -1c + 3c2 = -36 + -5c + 5c2 Solving for variable 'c'. Reorder the terms: -18 + 36 + -1c + 5c + 3c2 + -5c2 = -36 + -5c + 5c2 + 36 + 5c + -5c2 Combine like terms: -18 + 36 = 18 18 + -1c + 5c + 3c2 + -5c2 = -36 + -5c + 5c2 + 36 + 5c + -5c2 Combine like terms: -1c + 5c = 4c 18 + 4c + 3c2 + -5c2 = -36 + -5c + 5c2 + 36 + 5c + -5c2 Combine like terms: 3c2 + -5c2 = -2c2 18 + 4c + -2c2 = -36 + -5c + 5c2 + 36 + 5c + -5c2 Reorder the terms: 18 + 4c + -2c2 = -36 + 36 + -5c + 5c + 5c2 + -5c2 Combine like terms: -36 + 36 = 0 18 + 4c + -2c2 = 0 + -5c + 5c + 5c2 + -5c2 18 + 4c + -2c2 = -5c + 5c + 5c2 + -5c2 Combine like terms: -5c + 5c = 0 18 + 4c + -2c2 = 0 + 5c2 + -5c2 18 + 4c + -2c2 = 5c2 + -5c2 Combine like terms: 5c2 + -5c2 = 0 18 + 4c + -2c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 2c + -1c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + 2c + -1c2)' equal to zero and attempt to solve: Simplifying 9 + 2c + -1c2 = 0 Solving 9 + 2c + -1c2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + -2c + c2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -2c + 9 + c2 = 0 + 9 Reorder the terms: -9 + 9 + -2c + c2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2c + c2 = 0 + 9 -2c + c2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2c + c2 = 9 The c term is -2c. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2c + 1 + c2 = 9 + 1 Reorder the terms: 1 + -2c + c2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + -2c + c2 = 10 Factor a perfect square on the left side: (c + -1)(c + -1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (c + -1) equal to 3.16227766 and -3.16227766.Subproblem 1
c + -1 = 3.16227766 Simplifying c + -1 = 3.16227766 Reorder the terms: -1 + c = 3.16227766 Solving -1 + c = 3.16227766 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + c = 3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + c = 3.16227766 + 1 c = 3.16227766 + 1 Combine like terms: 3.16227766 + 1 = 4.16227766 c = 4.16227766 Simplifying c = 4.16227766Subproblem 2
c + -1 = -3.16227766 Simplifying c + -1 = -3.16227766 Reorder the terms: -1 + c = -3.16227766 Solving -1 + c = -3.16227766 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + c = -3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + c = -3.16227766 + 1 c = -3.16227766 + 1 Combine like terms: -3.16227766 + 1 = -2.16227766 c = -2.16227766 Simplifying c = -2.16227766Solution
The solution to the problem is based on the solutions from the subproblems. c = {4.16227766, -2.16227766}Solution
c = {4.16227766, -2.16227766}
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