Answer:
[tex] x = -4 + \sqrt{7} [/tex] and [tex] x = -4 - \sqrt{7} [/tex]
Step-by-step explanation:
The x-intercepts occur at y = 0.
0 = (x + 4)² - 7
x² + 8x + 16 - 7 = 0
x² + 8x + 9 = 0
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-8 \pm \sqrt{8^2 - 4(1)(9)}}{2(1)} [/tex]
[tex] x = \dfrac{-8 \pm \sqrt{64 - 36}}{2} [/tex]
[tex] x = \dfrac{-8 \pm \sqrt{28}}{2} [/tex]
[tex] x = \dfrac{-8 \pm 2\sqrt{7}}{2} [/tex]
[tex] x = -4 \pm \sqrt{7} [/tex]
[tex] x = -4 + \sqrt{7} [/tex] and [tex] x = -4 - \sqrt{7} [/tex]
