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Simplifying 15 + -5c(5c + -5) + -1c + 6 = 0 Reorder the terms: 15 + -5c(-5 + 5c) + -1c + 6 = 0 15 + (-5 * -5c + 5c * -5c) + -1c + 6 = 0 15 + (25c + -25c2) + -1c + 6 = 0 Reorder the terms: 15 + 6 + 25c + -1c + -25c2 = 0 Combine like terms: 15 + 6 = 21 21 + 25c + -1c + -25c2 = 0 Combine like terms: 25c + -1c = 24c 21 + 24c + -25c2 = 0 Solving 21 + 24c + -25c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -0.84 + -0.96c + c2 = 0 Move the constant term to the right: Add '0.84' to each side of the equation. -0.84 + -0.96c + 0.84 + c2 = 0 + 0.84 Reorder the terms: -0.84 + 0.84 + -0.96c + c2 = 0 + 0.84 Combine like terms: -0.84 + 0.84 = 0.00 0.00 + -0.96c + c2 = 0 + 0.84 -0.96c + c2 = 0 + 0.84 Combine like terms: 0 + 0.84 = 0.84 -0.96c + c2 = 0.84 The c term is -0.96c. Take half its coefficient (-0.48). Square it (0.2304) and add it to both sides. Add '0.2304' to each side of the equation. -0.96c + 0.2304 + c2 = 0.84 + 0.2304 Reorder the terms: 0.2304 + -0.96c + c2 = 0.84 + 0.2304 Combine like terms: 0.84 + 0.2304 = 1.0704 0.2304 + -0.96c + c2 = 1.0704 Factor a perfect square on the left side: (c + -0.48)(c + -0.48) = 1.0704 Calculate the square root of the right side: 1.034601373 Break this problem into two subproblems by setting (c + -0.48) equal to 1.034601373 and -1.034601373.Subproblem 1
c + -0.48 = 1.034601373 Simplifying c + -0.48 = 1.034601373 Reorder the terms: -0.48 + c = 1.034601373 Solving -0.48 + c = 1.034601373 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.48' to each side of the equation. -0.48 + 0.48 + c = 1.034601373 + 0.48 Combine like terms: -0.48 + 0.48 = 0.00 0.00 + c = 1.034601373 + 0.48 c = 1.034601373 + 0.48 Combine like terms: 1.034601373 + 0.48 = 1.514601373 c = 1.514601373 Simplifying c = 1.514601373Subproblem 2
c + -0.48 = -1.034601373 Simplifying c + -0.48 = -1.034601373 Reorder the terms: -0.48 + c = -1.034601373 Solving -0.48 + c = -1.034601373 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.48' to each side of the equation. -0.48 + 0.48 + c = -1.034601373 + 0.48 Combine like terms: -0.48 + 0.48 = 0.00 0.00 + c = -1.034601373 + 0.48 c = -1.034601373 + 0.48 Combine like terms: -1.034601373 + 0.48 = -0.554601373 c = -0.554601373 Simplifying c = -0.554601373Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.514601373, -0.554601373}
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