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Simplifying (3q2 + 8) + (7q2 + 4q + 2) = 0 Reorder the terms: (8 + 3q2) + (7q2 + 4q + 2) = 0 Remove parenthesis around (8 + 3q2) 8 + 3q2 + (7q2 + 4q + 2) = 0 Reorder the terms: 8 + 3q2 + (2 + 4q + 7q2) = 0 Remove parenthesis around (2 + 4q + 7q2) 8 + 3q2 + 2 + 4q + 7q2 = 0 Reorder the terms: 8 + 2 + 4q + 3q2 + 7q2 = 0 Combine like terms: 8 + 2 = 10 10 + 4q + 3q2 + 7q2 = 0 Combine like terms: 3q2 + 7q2 = 10q2 10 + 4q + 10q2 = 0 Solving 10 + 4q + 10q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 2q + 5q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 2q + 5q2)' equal to zero and attempt to solve: Simplifying 5 + 2q + 5q2 = 0 Solving 5 + 2q + 5q2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + 0.4q + q2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.4q + -1 + q2 = 0 + -1 Reorder the terms: 1 + -1 + 0.4q + q2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.4q + q2 = 0 + -1 0.4q + q2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.4q + q2 = -1 The q term is 0.4q. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4q + 0.04 + q2 = -1 + 0.04 Reorder the terms: 0.04 + 0.4q + q2 = -1 + 0.04 Combine like terms: -1 + 0.04 = -0.96 0.04 + 0.4q + q2 = -0.96 Factor a perfect square on the left side: (q + 0.2)(q + 0.2) = -0.96 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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