What is the solution set for`x^{2}-x-72=0`?

Answer 1

To solve the quadratic equation \( x^2 - x - 72 = 0 \), we can use the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

In this equation, \( a = 1 \), \( b = -1 \), and \( c = -72 \). Plugging in these values:

1. Calculate the discriminant:

\[ b^2 - 4ac = (-1)^2 - 4(1)(-72) = 1 + 288 = 289 \]

2. Calculate the square root of the discriminant:

\[ \sqrt{289} = 17 \]

3. Now plug this back into the quadratic formula:

\[ x = \frac{-(-1) \pm 17}{2(1)} = \frac{1 \pm 17}{2} \]

4. This gives us two solutions:

\[ x = \frac{1 + 17}{2} = \frac{18}{2} = 9 \]

\[ x = \frac{1 - 17}{2} = \frac{-16}{2} = -8 \]

Thus, the solution set for the equation \( x^2 - x - 72 = 0 \) is:

\[ { 9, -8 } \]