Solve for x.
–3 = 12x2 + 13x
(1 point)
a. x =three-fourths, one-third
b. x = –three-fourths, –one-third
c. x = 1, one-fourth
d. x = –1, –one-fourth
To solve the equation –3 = 12x^2 + 13x, we can start by rearranging the equation in standard quadratic form, which is ax^2 + bx + c = 0.
12x^2 + 13x + 3 = 0
Now, we can attempt to factor the quadratic equation, but it does not seem to easily factor.
To solve for x, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 12, b = 13, and c = 3. Plugging these values into the quadratic formula, we get:
x = (-13 ± √(13^2 - 4(12)(3))) / (2(12))
x = (-13 ± √(169 - 144)) / 24
x = (-13 ± √25) / 24
x = (-13 ± 5) / 24
Now we have two possible values for x:
x = (-13 + 5) / 24 = -8/24 = -1/3
x = (-13 - 5) / 24 = -18/24 = -3/4
So the solutions for x are x = -1/3 and x = -3/4.
Therefore, the correct answer is:
b. x = –three-fourths, –one-third