Question

Solve the given equation by factoring.

5a. x^2+2x+5=0

5b. 6x^2+7x+2=0

Answer 1

1. $x^{2} + 2x + 5 = 0$

$$x ^ {2} + 2 x + 1 - 1 + 5 = 0$$ $$(x + 1) ^ {2} = - 4$$ $$x + 1 = \pm \sqrt {- 4}$$ $$x + 1 = \pm 2 i$$ $$x _ {1} = 2 i - 1$$ $$x _ {2} = - 2 i - 1$$

2. $6x^{2} + 7x + 2 = 0$

$$a c = 1 2$$ $$6 x ^ {2} + 3 x + 4 x + 2 = 0$$ $$3 x (2 x + 1) + 2 (2 x + 1) = 0$$ $$(3 x + 2) (2 x + 1) = 0$$ $$x _ {1} = - \frac {2}{3} \quad x _ {2} = - \frac {1}{2}$$