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Simplifying 7(c + 7) * c = 8 Reorder the terms: 7(7 + c) * c = 8 Reorder the terms for easier multiplication: 7c(7 + c) = 8 (7 * 7c + c * 7c) = 8 (49c + 7c2) = 8 Solving 49c + 7c2 = 8 Solving for variable 'c'. Reorder the terms: -8 + 49c + 7c2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 49c + 7c2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + 7c + c2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 7c + 1.142857143 + c2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 7c + c2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 7c + c2 = 0 + 1.142857143 7c + c2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 7c + c2 = 1.142857143 The c term is 7c. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7c + 12.25 + c2 = 1.142857143 + 12.25 Reorder the terms: 12.25 + 7c + c2 = 1.142857143 + 12.25 Combine like terms: 1.142857143 + 12.25 = 13.392857143 12.25 + 7c + c2 = 13.392857143 Factor a perfect square on the left side: (c + 3.5)(c + 3.5) = 13.392857143 Calculate the square root of the right side: 3.659625274 Break this problem into two subproblems by setting (c + 3.5) equal to 3.659625274 and -3.659625274.Subproblem 1
c + 3.5 = 3.659625274 Simplifying c + 3.5 = 3.659625274 Reorder the terms: 3.5 + c = 3.659625274 Solving 3.5 + c = 3.659625274 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + c = 3.659625274 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + c = 3.659625274 + -3.5 c = 3.659625274 + -3.5 Combine like terms: 3.659625274 + -3.5 = 0.159625274 c = 0.159625274 Simplifying c = 0.159625274Subproblem 2
c + 3.5 = -3.659625274 Simplifying c + 3.5 = -3.659625274 Reorder the terms: 3.5 + c = -3.659625274 Solving 3.5 + c = -3.659625274 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + c = -3.659625274 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + c = -3.659625274 + -3.5 c = -3.659625274 + -3.5 Combine like terms: -3.659625274 + -3.5 = -7.159625274 c = -7.159625274 Simplifying c = -7.159625274Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.159625274, -7.159625274}
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