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Beyond the Answer
To solve \( m^{2}+m-90 = 0 \), we can use the quadratic formula: \( m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 1 \), and \( c = -90 \). Plugging in these values gives us \( m = \frac{-1 \pm \sqrt{1 + 360}}{2} = \frac{-1 \pm 19}{2} \). This results in two potential roots: \( m = 9 \) and \( m = -10 \). These roots are highly relatable, as they can represent real-world situations. For instance, \( m \) could symbolize the number of items produced beyond a threshold of 90 units. If you were running a production line, knowing how many additional units to produce could directly affect your profits! The two values are like two different business strategies: one success (an extra 9 units) and the other a lesson learned (a deficit of 10 units).
