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Simplifying c2 + 10c + -9 = 0 Reorder the terms: -9 + 10c + c2 = 0 Solving -9 + 10c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 10c + 9 + c2 = 0 + 9 Reorder the terms: -9 + 9 + 10c + c2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 10c + c2 = 0 + 9 10c + c2 = 0 + 9 Combine like terms: 0 + 9 = 9 10c + c2 = 9 The c term is 10c. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10c + 25 + c2 = 9 + 25 Reorder the terms: 25 + 10c + c2 = 9 + 25 Combine like terms: 9 + 25 = 34 25 + 10c + c2 = 34 Factor a perfect square on the left side: (c + 5)(c + 5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (c + 5) equal to 5.830951895 and -5.830951895.Subproblem 1
c + 5 = 5.830951895 Simplifying c + 5 = 5.830951895 Reorder the terms: 5 + c = 5.830951895 Solving 5 + c = 5.830951895 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + c = 5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + c = 5.830951895 + -5 c = 5.830951895 + -5 Combine like terms: 5.830951895 + -5 = 0.830951895 c = 0.830951895 Simplifying c = 0.830951895Subproblem 2
c + 5 = -5.830951895 Simplifying c + 5 = -5.830951895 Reorder the terms: 5 + c = -5.830951895 Solving 5 + c = -5.830951895 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + c = -5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + c = -5.830951895 + -5 c = -5.830951895 + -5 Combine like terms: -5.830951895 + -5 = -10.830951895 c = -10.830951895 Simplifying c = -10.830951895Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.830951895, -10.830951895}
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