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Simplifying (10q + -3)(q + 11) = 0 Reorder the terms: (-3 + 10q)(q + 11) = 0 Reorder the terms: (-3 + 10q)(11 + q) = 0 Multiply (-3 + 10q) * (11 + q) (-3(11 + q) + 10q * (11 + q)) = 0 ((11 * -3 + q * -3) + 10q * (11 + q)) = 0 ((-33 + -3q) + 10q * (11 + q)) = 0 (-33 + -3q + (11 * 10q + q * 10q)) = 0 (-33 + -3q + (110q + 10q2)) = 0 Combine like terms: -3q + 110q = 107q (-33 + 107q + 10q2) = 0 Solving -33 + 107q + 10q2 = 0 Solving for variable 'q'. Factor a trinomial. (-11 + -1q)(3 + -10q) = 0Subproblem 1
Set the factor '(-11 + -1q)' equal to zero and attempt to solve: Simplifying -11 + -1q = 0 Solving -11 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1q = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1q = 0 + 11 -1q = 0 + 11 Combine like terms: 0 + 11 = 11 -1q = 11 Divide each side by '-1'. q = -11 Simplifying q = -11Subproblem 2
Set the factor '(3 + -10q)' equal to zero and attempt to solve: Simplifying 3 + -10q = 0 Solving 3 + -10q = 0 Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -10q = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -10q = 0 + -3 -10q = 0 + -3 Combine like terms: 0 + -3 = -3 -10q = -3 Divide each side by '-10'. q = 0.3 Simplifying q = 0.3Solution
q = {-11, 0.3}
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