To solve the equation \( x^2 = -11x + 4 \), we first rearrange it to standard quadratic form:
\[ x^2 + 11x - 4 = 0 \]
Now we can apply the quadratic formula, which states:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In our equation, \( a = 1 \), \( b = 11 \), and \( c = -4 \).
- Calculate the discriminant:
\[ b^2 - 4ac = 11^2 - 4(1)(-4) = 121 + 16 = 137 \]
- Plugging the values into the quadratic formula gives us:
\[ x = \frac{-11 \pm \sqrt{137}}{2(1)} = \frac{-11 \pm \sqrt{137}}{2} \]
So, the solutions are:
\[ x = \frac{-11 - \sqrt{137}}{2}, \quad x = \frac{-11 + \sqrt{137}}{2} \]
Thus, these correspond to the answer:
\[ \frac{-11 - \sqrt{137}}{2}, \quad \frac{-11 + \sqrt{137}}{2} \]
So the solution is:
StartFraction negative 11 minus StartRoot 137 EndRoot Over 2 EndFraction comma StartFraction negative 11 plus StartRoot 137 EndRoot Over 2 EndFraction