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Simplifying 25 + -7c + -16c2 = 0 Solving 25 + -7c + -16c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -1.5625 + 0.4375c + c2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + 0.4375c + 1.5625 + c2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + 0.4375c + c2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + 0.4375c + c2 = 0 + 1.5625 0.4375c + c2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 0.4375c + c2 = 1.5625 The c term is 0.4375c. Take half its coefficient (0.21875). Square it (0.0478515625) and add it to both sides. Add '0.0478515625' to each side of the equation. 0.4375c + 0.0478515625 + c2 = 1.5625 + 0.0478515625 Reorder the terms: 0.0478515625 + 0.4375c + c2 = 1.5625 + 0.0478515625 Combine like terms: 1.5625 + 0.0478515625 = 1.6103515625 0.0478515625 + 0.4375c + c2 = 1.6103515625 Factor a perfect square on the left side: (c + 0.21875)(c + 0.21875) = 1.6103515625 Calculate the square root of the right side: 1.268996282 Break this problem into two subproblems by setting (c + 0.21875) equal to 1.268996282 and -1.268996282.Subproblem 1
c + 0.21875 = 1.268996282 Simplifying c + 0.21875 = 1.268996282 Reorder the terms: 0.21875 + c = 1.268996282 Solving 0.21875 + c = 1.268996282 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.21875' to each side of the equation. 0.21875 + -0.21875 + c = 1.268996282 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + c = 1.268996282 + -0.21875 c = 1.268996282 + -0.21875 Combine like terms: 1.268996282 + -0.21875 = 1.050246282 c = 1.050246282 Simplifying c = 1.050246282Subproblem 2
c + 0.21875 = -1.268996282 Simplifying c + 0.21875 = -1.268996282 Reorder the terms: 0.21875 + c = -1.268996282 Solving 0.21875 + c = -1.268996282 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.21875' to each side of the equation. 0.21875 + -0.21875 + c = -1.268996282 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + c = -1.268996282 + -0.21875 c = -1.268996282 + -0.21875 Combine like terms: -1.268996282 + -0.21875 = -1.487746282 c = -1.487746282 Simplifying c = -1.487746282Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.050246282, -1.487746282}
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