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Simplifying c2 + -26c + -56 = 9 Reorder the terms: -56 + -26c + c2 = 9 Solving -56 + -26c + c2 = 9 Solving for variable 'c'. Reorder the terms: -56 + -9 + -26c + c2 = 9 + -9 Combine like terms: -56 + -9 = -65 -65 + -26c + c2 = 9 + -9 Combine like terms: 9 + -9 = 0 -65 + -26c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + -26c + 65 + c2 = 0 + 65 Reorder the terms: -65 + 65 + -26c + c2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + -26c + c2 = 0 + 65 -26c + c2 = 0 + 65 Combine like terms: 0 + 65 = 65 -26c + c2 = 65 The c term is -26c. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26c + 169 + c2 = 65 + 169 Reorder the terms: 169 + -26c + c2 = 65 + 169 Combine like terms: 65 + 169 = 234 169 + -26c + c2 = 234 Factor a perfect square on the left side: (c + -13)(c + -13) = 234 Calculate the square root of the right side: 15.297058541 Break this problem into two subproblems by setting (c + -13) equal to 15.297058541 and -15.297058541.Subproblem 1
c + -13 = 15.297058541 Simplifying c + -13 = 15.297058541 Reorder the terms: -13 + c = 15.297058541 Solving -13 + c = 15.297058541 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + c = 15.297058541 + 13 Combine like terms: -13 + 13 = 0 0 + c = 15.297058541 + 13 c = 15.297058541 + 13 Combine like terms: 15.297058541 + 13 = 28.297058541 c = 28.297058541 Simplifying c = 28.297058541Subproblem 2
c + -13 = -15.297058541 Simplifying c + -13 = -15.297058541 Reorder the terms: -13 + c = -15.297058541 Solving -13 + c = -15.297058541 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + c = -15.297058541 + 13 Combine like terms: -13 + 13 = 0 0 + c = -15.297058541 + 13 c = -15.297058541 + 13 Combine like terms: -15.297058541 + 13 = -2.297058541 c = -2.297058541 Simplifying c = -2.297058541Solution
The solution to the problem is based on the solutions from the subproblems. c = {28.297058541, -2.297058541}
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