Solve the equation by a method of your choice:
6x2 + 5x + 1 = 0
If there are two solutions, separate the solutions by a comma.
Easy to see that it factors, so that is the obvious choice
6x^2 + 5x + 1 = 0
(2x+1)(3x+1) = 0
x = -1/2 or x = -1/3
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To solve the equation 6x^2 + 5x + 1 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our given equation, we have a = 6, b = 5, and c = 1. Plugging these values into the quadratic formula, we can find the solutions for x:
x = (-5 ± √(5^2 - 4*6*1)) / (2*6)
x = (-5 ± √(25 - 24)) / 12
x = (-5 ± √1) / 12
Now let's simplify further:
x = (-5 ± 1) / 12
This gives us two possible solutions:
1) x = (-5 + 1) / 12
x = -4/12
x = -1/3
2) x = (-5 - 1) / 12
x = -6/12
x = -1/2
Therefore, the solutions to the equation 6x^2 + 5x + 1 = 0 are x = -1/3 and x = -1/2.