Question

Solve by Completing the Square

5. x^2+14x+13=0

6. 5x^2-12x= -2

Answer 1

$$5. x ^ {\wedge} 2 + 14x + 13 = 0$$ $$x^{2} + 14x + 13 = 0$$ $$x^{2} + 14x + 49 - 49 + 13 = 0$$ $$(x + 7)^{2} = 36$$ $$(x + 7) = \pm 6$$ $$x_{1} = -1 \text{ and } x_{2} = -13$$ $$6. 5x^{\wedge}2 - 12x = -2$$ $$5x^{2} - 12x + 2 = 0$$ $$5(x^{2} - 2.4x + .4) = 0$$ $$5(x^{2} - 2.4x + 1.44 - 1.44 + .4) = 0$$ $$x^{2} - 2.4x + 1.44 - 1.04 = 0$$ $$(x - 1.2)^{2} = 1.04$$ $$(x - 1.2) = \pm 1.02$$ $$x_{1} = .18 \text{ and } x_{2} = 2.22$$