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Simplifying (10q + 7)(q + -10) = 0 Reorder the terms: (7 + 10q)(q + -10) = 0 Reorder the terms: (7 + 10q)(-10 + q) = 0 Multiply (7 + 10q) * (-10 + q) (7(-10 + q) + 10q * (-10 + q)) = 0 ((-10 * 7 + q * 7) + 10q * (-10 + q)) = 0 ((-70 + 7q) + 10q * (-10 + q)) = 0 (-70 + 7q + (-10 * 10q + q * 10q)) = 0 (-70 + 7q + (-100q + 10q2)) = 0 Combine like terms: 7q + -100q = -93q (-70 + -93q + 10q2) = 0 Solving -70 + -93q + 10q2 = 0 Solving for variable 'q'. Factor a trinomial. (-7 + -10q)(10 + -1q) = 0Subproblem 1
Set the factor '(-7 + -10q)' equal to zero and attempt to solve: Simplifying -7 + -10q = 0 Solving -7 + -10q = 0 Move all terms containing q to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -10q = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -10q = 0 + 7 -10q = 0 + 7 Combine like terms: 0 + 7 = 7 -10q = 7 Divide each side by '-10'. q = -0.7 Simplifying q = -0.7Subproblem 2
Set the factor '(10 + -1q)' equal to zero and attempt to solve: Simplifying 10 + -1q = 0 Solving 10 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1q = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1q = 0 + -10 -1q = 0 + -10 Combine like terms: 0 + -10 = -10 -1q = -10 Divide each side by '-1'. q = 10 Simplifying q = 10Solution
q = {-0.7, 10}
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