Respuesta :
Answer:
1. [tex]x=-\frac{3+\sqrt{3}}{3}\text{ (or) }x=\frac{-3+\sqrt{3}}{3}[/tex]
2. Quadratic formula is the most efficient way to solve this equation.
Step-by-step explanation:
We have been given an equation [tex]3x^2+6x+8 = 6[/tex]. We are asked to solve our given equation using quadratic formula.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex], where,
b = Coefficient of x term,
c = Constant,
a = Coefficient of [tex]x^2[/tex] term.
[tex]3x^2+6x+8-6=6-6[/tex]
[tex]3x^2+6x+2=0[/tex]
Upon substituting our given values, we will get:
[tex]x=\frac{-6\pm\sqrt{6^2-4(3)(2)}}{2(3)}[/tex]
[tex]x=\frac{-6\pm\sqrt{36-24}}{6}[/tex]
[tex]x=\frac{-6\pm\sqrt{12}}{6}[/tex]
[tex]x=\frac{-6\pm \sqrt{4\cdot 3}}{6}[/tex]
[tex]x=\frac{-6\pm 2\sqrt{3}}{6}[/tex]
[tex]x=\frac{-6-2\sqrt{3}}{6}\text{ (or) }x=\frac{-6+2\sqrt{3}}{6}[/tex]
[tex]x=\frac{-2(3+\sqrt{3})}{2*3}\text{ (or) }x=\frac{2(-3+\sqrt{3})}{2*3}[/tex]
[tex]x=-\frac{3+\sqrt{3}}{3}\text{ (or) }x=\frac{-3+\sqrt{3}}{3}[/tex]
Therefore, the solutions for our given equation are [tex]x=-\frac{3+\sqrt{3}}{3}\text{ (or) }x=\frac{-3+\sqrt{3}}{3}[/tex].
2. We cannot factor our given equation by splitting the middle term because there are no such numbers which add up-to 6 and whose product is 6.
Therefore, the quadratic formula is the most efficient way to solve this equation.
