x^2 = 7x + 4
x^2 - 7x - 4 = 0
This polynomial is not factorable, so we can use the quadratic formula with a = 1, b = -7, and c = -4
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-(-7) \pm \sqrt{(-7)^2 - 4(1)(-4)}}{2(1)} [/tex]
[tex] x = \dfrac{7 \pm \sqrt{49 + 16}}{2} [/tex]
[tex] x = \dfrac{7 \pm \sqrt{65}}{2} [/tex]
[tex] x = \dfrac{7}{2} + \dfrac{\sqrt{65}}{2} [/tex] or [tex] x = \dfrac{7}{2} - \dfrac{\sqrt{65}}{2} [/tex]
