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Simplifying c2 + -4c + -16 = 4 Reorder the terms: -16 + -4c + c2 = 4 Solving -16 + -4c + c2 = 4 Solving for variable 'c'. Reorder the terms: -16 + -4 + -4c + c2 = 4 + -4 Combine like terms: -16 + -4 = -20 -20 + -4c + c2 = 4 + -4 Combine like terms: 4 + -4 = 0 -20 + -4c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -4c + 20 + c2 = 0 + 20 Reorder the terms: -20 + 20 + -4c + c2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -4c + c2 = 0 + 20 -4c + c2 = 0 + 20 Combine like terms: 0 + 20 = 20 -4c + c2 = 20 The c term is -4c. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4c + 4 + c2 = 20 + 4 Reorder the terms: 4 + -4c + c2 = 20 + 4 Combine like terms: 20 + 4 = 24 4 + -4c + c2 = 24 Factor a perfect square on the left side: (c + -2)(c + -2) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (c + -2) equal to 4.898979486 and -4.898979486.Subproblem 1
c + -2 = 4.898979486 Simplifying c + -2 = 4.898979486 Reorder the terms: -2 + c = 4.898979486 Solving -2 + c = 4.898979486 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c = 4.898979486 + 2 Combine like terms: -2 + 2 = 0 0 + c = 4.898979486 + 2 c = 4.898979486 + 2 Combine like terms: 4.898979486 + 2 = 6.898979486 c = 6.898979486 Simplifying c = 6.898979486Subproblem 2
c + -2 = -4.898979486 Simplifying c + -2 = -4.898979486 Reorder the terms: -2 + c = -4.898979486 Solving -2 + c = -4.898979486 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c = -4.898979486 + 2 Combine like terms: -2 + 2 = 0 0 + c = -4.898979486 + 2 c = -4.898979486 + 2 Combine like terms: -4.898979486 + 2 = -2.898979486 c = -2.898979486 Simplifying c = -2.898979486Solution
The solution to the problem is based on the solutions from the subproblems. c = {6.898979486, -2.898979486}
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