Answer:
[tex] x = -\dfrac{3}{2} + \dfrac{\sqrt{11}}{2}i [/tex] or [tex] x = -\dfrac{3}{2} - \dfrac{\sqrt{11}}{2}i [/tex]
Step-by-step explanation:
[tex] 14x^2 + 42x + 70 = 0 [/tex]
First, divide both sides by 14.
[tex] x^2 + 3x + 5 = 0 [/tex]
There are no two real numbers whose product is 5 and whose sum is 3, so this polynomial is not factorable. We use the quadratic formula.
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
We have a = 1; b = 3; c = 5.
[tex] x = \dfrac{-3 \pm \sqrt{(-3)^2 - 4(1)(5)}}{2(1)} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{9 - 20}}{2} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{-11}}{2} [/tex]
[tex] x = \dfrac{-3 \pm i\sqrt{11}}{2} [/tex]
[tex] x = -\dfrac{3}{2} + \dfrac{\sqrt{11}}{2}i [/tex] or [tex] x = -\dfrac{3}{2} - \dfrac{\sqrt{11}}{2}i [/tex]
