Question

find the solution set.
6x² + 7x + 2 = 0
separate the two values with a comma.
enter the correct answer.

Explanation:

Step1: Factor the quadratic equation

We need two numbers that multiply to $6\times2=12$ and add to $7$. These numbers are $3$ and $4$. Split the middle term:
$6x^2 + 3x + 4x + 2 = 0$
Factor by grouping:
$3x(2x + 1) + 2(2x + 1) = 0$
$(3x + 2)(2x + 1) = 0$

Step2: Solve for $x$ individually

Set each factor equal to 0:

Substep2a: Solve $3x+2=0$

$3x = -2$
$x = -\frac{2}{3}$

Substep2b: Solve $2x+1=0$

$2x = -1$
$x = -\frac{1}{2}$

Answer:

$-\frac{2}{3}, -\frac{1}{2}$