Question

1. Solve the following equation using the quadratic formula: 3x2 + 6x + 8 = 6.

Answer 1

Answer:

1. $x=-\frac{3+\sqrt{3}}{3}\text{ (or) }x=\frac{-3+\sqrt{3}}{3}$

2. Quadratic formula is the most efficient way to solve this equation.

Step-by-step explanation:

We have been given an equation $3x^2+6x+8 = 6$. We are asked to solve our given equation using quadratic formula.

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$, where,

b = Coefficient of x term,

c = Constant,

a = Coefficient of $x^2$ term.

$3x^2+6x+8-6=6-6$

$3x^2+6x+2=0$

Upon substituting our given values, we will get:

$x=\frac{-6\pm\sqrt{6^2-4(3)(2)}}{2(3)}$

$x=\frac{-6\pm\sqrt{36-24}}{6}$

$x=\frac{-6\pm\sqrt{12}}{6}$

$x=\frac{-6\pm \sqrt{4\cdot 3}}{6}$

$x=\frac{-6\pm 2\sqrt{3}}{6}$

$x=\frac{-6-2\sqrt{3}}{6}\text{ (or) }x=\frac{-6+2\sqrt{3}}{6}$

$x=\frac{-2(3+\sqrt{3})}{2*3}\text{ (or) }x=\frac{2(-3+\sqrt{3})}{2*3}$

$x=-\frac{3+\sqrt{3}}{3}\text{ (or) }x=\frac{-3+\sqrt{3}}{3}$

Therefore, the solutions for our given equation are $x=-\frac{3+\sqrt{3}}{3}\text{ (or) }x=\frac{-3+\sqrt{3}}{3}$.

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.