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Simplifying 8c(c + -5) + -3c = 15 Reorder the terms: 8c(-5 + c) + -3c = 15 (-5 * 8c + c * 8c) + -3c = 15 (-40c + 8c2) + -3c = 15 Reorder the terms: -40c + -3c + 8c2 = 15 Combine like terms: -40c + -3c = -43c -43c + 8c2 = 15 Solving -43c + 8c2 = 15 Solving for variable 'c'. Reorder the terms: -15 + -43c + 8c2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -43c + 8c2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + -5.375c + c2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -5.375c + 1.875 + c2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -5.375c + c2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -5.375c + c2 = 0 + 1.875 -5.375c + c2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -5.375c + c2 = 1.875 The c term is -5.375c. Take half its coefficient (-2.6875). Square it (7.22265625) and add it to both sides. Add '7.22265625' to each side of the equation. -5.375c + 7.22265625 + c2 = 1.875 + 7.22265625 Reorder the terms: 7.22265625 + -5.375c + c2 = 1.875 + 7.22265625 Combine like terms: 1.875 + 7.22265625 = 9.09765625 7.22265625 + -5.375c + c2 = 9.09765625 Factor a perfect square on the left side: (c + -2.6875)(c + -2.6875) = 9.09765625 Calculate the square root of the right side: 3.016232128 Break this problem into two subproblems by setting (c + -2.6875) equal to 3.016232128 and -3.016232128.Subproblem 1
c + -2.6875 = 3.016232128 Simplifying c + -2.6875 = 3.016232128 Reorder the terms: -2.6875 + c = 3.016232128 Solving -2.6875 + c = 3.016232128 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.6875' to each side of the equation. -2.6875 + 2.6875 + c = 3.016232128 + 2.6875 Combine like terms: -2.6875 + 2.6875 = 0.0000 0.0000 + c = 3.016232128 + 2.6875 c = 3.016232128 + 2.6875 Combine like terms: 3.016232128 + 2.6875 = 5.703732128 c = 5.703732128 Simplifying c = 5.703732128Subproblem 2
c + -2.6875 = -3.016232128 Simplifying c + -2.6875 = -3.016232128 Reorder the terms: -2.6875 + c = -3.016232128 Solving -2.6875 + c = -3.016232128 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2.6875' to each side of the equation. -2.6875 + 2.6875 + c = -3.016232128 + 2.6875 Combine like terms: -2.6875 + 2.6875 = 0.0000 0.0000 + c = -3.016232128 + 2.6875 c = -3.016232128 + 2.6875 Combine like terms: -3.016232128 + 2.6875 = -0.328732128 c = -0.328732128 Simplifying c = -0.328732128Solution
The solution to the problem is based on the solutions from the subproblems. c = {5.703732128, -0.328732128}
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