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Simplifying 2q(2q) + 22q = -60 Remove parenthesis around (2q) 2q * 2q + 22q = -60 Reorder the terms for easier multiplication: 2 * 2q * q + 22q = -60 Multiply 2 * 2 4q * q + 22q = -60 Multiply q * q 4q2 + 22q = -60 Reorder the terms: 22q + 4q2 = -60 Solving 22q + 4q2 = -60 Solving for variable 'q'. Reorder the terms: 60 + 22q + 4q2 = -60 + 60 Combine like terms: -60 + 60 = 0 60 + 22q + 4q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(30 + 11q + 2q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(30 + 11q + 2q2)' equal to zero and attempt to solve: Simplifying 30 + 11q + 2q2 = 0 Solving 30 + 11q + 2q2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 15 + 5.5q + q2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + 5.5q + -15 + q2 = 0 + -15 Reorder the terms: 15 + -15 + 5.5q + q2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 5.5q + q2 = 0 + -15 5.5q + q2 = 0 + -15 Combine like terms: 0 + -15 = -15 5.5q + q2 = -15 The q term is 5.5q. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5q + 7.5625 + q2 = -15 + 7.5625 Reorder the terms: 7.5625 + 5.5q + q2 = -15 + 7.5625 Combine like terms: -15 + 7.5625 = -7.4375 7.5625 + 5.5q + q2 = -7.4375 Factor a perfect square on the left side: (q + 2.75)(q + 2.75) = -7.4375 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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