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Simplifying 15c(5c + -7) = 2c + -9 Reorder the terms: 15c(-7 + 5c) = 2c + -9 (-7 * 15c + 5c * 15c) = 2c + -9 (-105c + 75c2) = 2c + -9 Reorder the terms: -105c + 75c2 = -9 + 2c Solving -105c + 75c2 = -9 + 2c Solving for variable 'c'. Reorder the terms: 9 + -105c + -2c + 75c2 = -9 + 2c + 9 + -2c Combine like terms: -105c + -2c = -107c 9 + -107c + 75c2 = -9 + 2c + 9 + -2c Reorder the terms: 9 + -107c + 75c2 = -9 + 9 + 2c + -2c Combine like terms: -9 + 9 = 0 9 + -107c + 75c2 = 0 + 2c + -2c 9 + -107c + 75c2 = 2c + -2c Combine like terms: 2c + -2c = 0 9 + -107c + 75c2 = 0 Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. 0.12 + -1.426666667c + c2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + -1.426666667c + -0.12 + c2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + -1.426666667c + c2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + -1.426666667c + c2 = 0 + -0.12 -1.426666667c + c2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 -1.426666667c + c2 = -0.12 The c term is -1.426666667c. Take half its coefficient (-0.7133333335). Square it (0.5088444447) and add it to both sides. Add '0.5088444447' to each side of the equation. -1.426666667c + 0.5088444447 + c2 = -0.12 + 0.5088444447 Reorder the terms: 0.5088444447 + -1.426666667c + c2 = -0.12 + 0.5088444447 Combine like terms: -0.12 + 0.5088444447 = 0.3888444447 0.5088444447 + -1.426666667c + c2 = 0.3888444447 Factor a perfect square on the left side: (c + -0.7133333335)(c + -0.7133333335) = 0.3888444447 Calculate the square root of the right side: 0.623573929 Break this problem into two subproblems by setting (c + -0.7133333335) equal to 0.623573929 and -0.623573929.Subproblem 1
c + -0.7133333335 = 0.623573929 Simplifying c + -0.7133333335 = 0.623573929 Reorder the terms: -0.7133333335 + c = 0.623573929 Solving -0.7133333335 + c = 0.623573929 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.7133333335' to each side of the equation. -0.7133333335 + 0.7133333335 + c = 0.623573929 + 0.7133333335 Combine like terms: -0.7133333335 + 0.7133333335 = 0.0000000000 0.0000000000 + c = 0.623573929 + 0.7133333335 c = 0.623573929 + 0.7133333335 Combine like terms: 0.623573929 + 0.7133333335 = 1.3369072625 c = 1.3369072625 Simplifying c = 1.3369072625Subproblem 2
c + -0.7133333335 = -0.623573929 Simplifying c + -0.7133333335 = -0.623573929 Reorder the terms: -0.7133333335 + c = -0.623573929 Solving -0.7133333335 + c = -0.623573929 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.7133333335' to each side of the equation. -0.7133333335 + 0.7133333335 + c = -0.623573929 + 0.7133333335 Combine like terms: -0.7133333335 + 0.7133333335 = 0.0000000000 0.0000000000 + c = -0.623573929 + 0.7133333335 c = -0.623573929 + 0.7133333335 Combine like terms: -0.623573929 + 0.7133333335 = 0.0897594045 c = 0.0897594045 Simplifying c = 0.0897594045Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.3369072625, 0.0897594045}
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