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Simplifying c(c + -4) = 9 Reorder the terms: c(-4 + c) = 9 (-4 * c + c * c) = 9 (-4c + c2) = 9 Solving -4c + c2 = 9 Solving for variable 'c'. Reorder the terms: -9 + -4c + c2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -4c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -4c + 9 + c2 = 0 + 9 Reorder the terms: -9 + 9 + -4c + c2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4c + c2 = 0 + 9 -4c + c2 = 0 + 9 Combine like terms: 0 + 9 = 9 -4c + c2 = 9 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 = 9 + 4 Reorder the terms: 4 + -4c + c2 = 9 + 4 Combine like terms: 9 + 4 = 13 4 + -4c + c2 = 13 Factor a perfect square on the left side: (c + -2)(c + -2) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (c + -2) equal to 3.605551275 and -3.605551275.Subproblem 1
c + -2 = 3.605551275 Simplifying c + -2 = 3.605551275 Reorder the terms: -2 + c = 3.605551275 Solving -2 + c = 3.605551275 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 = 3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + c = 3.605551275 + 2 c = 3.605551275 + 2 Combine like terms: 3.605551275 + 2 = 5.605551275 c = 5.605551275 Simplifying c = 5.605551275Subproblem 2
c + -2 = -3.605551275 Simplifying c + -2 = -3.605551275 Reorder the terms: -2 + c = -3.605551275 Solving -2 + c = -3.605551275 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 = -3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + c = -3.605551275 + 2 c = -3.605551275 + 2 Combine like terms: -3.605551275 + 2 = -1.605551275 c = -1.605551275 Simplifying c = -1.605551275Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.605551275, -1.605551275}
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