Answer:
[tex] x = 2 + \sqrt{42} [/tex] or [tex] x = 2 - \sqrt{42} [/tex]
Step-by-step explanation:
[tex] x^2 - 4x - 9 = 29 [/tex]
Subtract 29 from both sides.
[tex] x^2 - 4x - 9 - 29 = 29 - 29 [/tex]
[tex] x^2 - 4x - 38 = 0 [/tex]
There are no two integers whose sum is -4 and whose product is -38, so the trinomial is not factorable. We can use the quadratic formula.
a = 1; b = -4; c = -38
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-38)}}{2(1)} [/tex]
[tex] x = \dfrac{4 \pm \sqrt{16 + 152}}{2} [/tex]
[tex] x = \dfrac{4 \pm \sqrt{168}}{2} [/tex]
[tex] x = 2 \pm \dfrac{\sqrt{4 \times 42}}{2} [/tex]
[tex] x = 2 \pm \dfrac{2\sqrt{42}}{2} [/tex]
[tex] x = 2 \pm \sqrt{42} [/tex]
[tex] x = 2 + \sqrt{42} [/tex] or [tex] x = 2 - \sqrt{42} [/tex]
