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Simplifying -5c(-4c + -7) + -5(-2c + -9) = 0 Reorder the terms: -5c(-7 + -4c) + -5(-2c + -9) = 0 (-7 * -5c + -4c * -5c) + -5(-2c + -9) = 0 (35c + 20c2) + -5(-2c + -9) = 0 Reorder the terms: 35c + 20c2 + -5(-9 + -2c) = 0 35c + 20c2 + (-9 * -5 + -2c * -5) = 0 35c + 20c2 + (45 + 10c) = 0 Reorder the terms: 45 + 35c + 10c + 20c2 = 0 Combine like terms: 35c + 10c = 45c 45 + 45c + 20c2 = 0 Solving 45 + 45c + 20c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '5'. 5(9 + 9c + 4c2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(9 + 9c + 4c2)' equal to zero and attempt to solve: Simplifying 9 + 9c + 4c2 = 0 Solving 9 + 9c + 4c2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 2.25c + c2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 2.25c + -2.25 + c2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 2.25c + c2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 2.25c + c2 = 0 + -2.25 2.25c + c2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 2.25c + c2 = -2.25 The c term is 2.25c. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25c + 1.265625 + c2 = -2.25 + 1.265625 Reorder the terms: 1.265625 + 2.25c + c2 = -2.25 + 1.265625 Combine like terms: -2.25 + 1.265625 = -0.984375 1.265625 + 2.25c + c2 = -0.984375 Factor a perfect square on the left side: (c + 1.125)(c + 1.125) = -0.984375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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