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Simplifying 5(q + 2) * 3q = -22 Reorder the terms: 5(2 + q) * 3q = -22 Reorder the terms for easier multiplication: 5 * 3q(2 + q) = -22 Multiply 5 * 3 15q(2 + q) = -22 (2 * 15q + q * 15q) = -22 (30q + 15q2) = -22 Solving 30q + 15q2 = -22 Solving for variable 'q'. Reorder the terms: 22 + 30q + 15q2 = -22 + 22 Combine like terms: -22 + 22 = 0 22 + 30q + 15q2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 1.466666667 + 2q + q2 = 0 Move the constant term to the right: Add '-1.466666667' to each side of the equation. 1.466666667 + 2q + -1.466666667 + q2 = 0 + -1.466666667 Reorder the terms: 1.466666667 + -1.466666667 + 2q + q2 = 0 + -1.466666667 Combine like terms: 1.466666667 + -1.466666667 = 0.000000000 0.000000000 + 2q + q2 = 0 + -1.466666667 2q + q2 = 0 + -1.466666667 Combine like terms: 0 + -1.466666667 = -1.466666667 2q + q2 = -1.466666667 The q term is 2q. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2q + 1 + q2 = -1.466666667 + 1 Reorder the terms: 1 + 2q + q2 = -1.466666667 + 1 Combine like terms: -1.466666667 + 1 = -0.466666667 1 + 2q + q2 = -0.466666667 Factor a perfect square on the left side: (q + 1)(q + 1) = -0.466666667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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