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Simplifying c2 + 8c + -9 = -6 Reorder the terms: -9 + 8c + c2 = -6 Solving -9 + 8c + c2 = -6 Solving for variable 'c'. Reorder the terms: -9 + 6 + 8c + c2 = -6 + 6 Combine like terms: -9 + 6 = -3 -3 + 8c + c2 = -6 + 6 Combine like terms: -6 + 6 = 0 -3 + 8c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 8c + 3 + c2 = 0 + 3 Reorder the terms: -3 + 3 + 8c + c2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 8c + c2 = 0 + 3 8c + c2 = 0 + 3 Combine like terms: 0 + 3 = 3 8c + c2 = 3 The c term is 8c. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8c + 16 + c2 = 3 + 16 Reorder the terms: 16 + 8c + c2 = 3 + 16 Combine like terms: 3 + 16 = 19 16 + 8c + c2 = 19 Factor a perfect square on the left side: (c + 4)(c + 4) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (c + 4) equal to 4.358898944 and -4.358898944.Subproblem 1
c + 4 = 4.358898944 Simplifying c + 4 = 4.358898944 Reorder the terms: 4 + c = 4.358898944 Solving 4 + c = 4.358898944 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + c = 4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + c = 4.358898944 + -4 c = 4.358898944 + -4 Combine like terms: 4.358898944 + -4 = 0.358898944 c = 0.358898944 Simplifying c = 0.358898944Subproblem 2
c + 4 = -4.358898944 Simplifying c + 4 = -4.358898944 Reorder the terms: 4 + c = -4.358898944 Solving 4 + c = -4.358898944 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + c = -4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + c = -4.358898944 + -4 c = -4.358898944 + -4 Combine like terms: -4.358898944 + -4 = -8.358898944 c = -8.358898944 Simplifying c = -8.358898944Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.358898944, -8.358898944}
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