First try to solve the equation by factoring. If you are unable to solve the equation by factoring, solve the equation by using the quadratic formula. For equations with solutions that are irrational numbers, give exact solutions and approximate solutions to the nearest thousandth.
42y^2 − 6 = 29y
42y^2 − 6 = 29y
42y^2 - 29y - 6 = 0
(6y+1)(7y-6) = 0
...
are the final answers are 0.808301, -0.117825
Oh, please!
(6y+1)(7y-6) = 0
so, either
6y+1 = 0
y = -1/6
or
7y-6 = 0
y = 6/7
How did you come up with your answers?
To solve the equation 42y^2 - 6 = 29y, we can factorize it by moving all terms to one side of the equation:
42y^2 - 29y - 6 = 0
Now, we can try to factorize the quadratic expression. However, in this case, factoring might not be straightforward, so we'll resort to using the quadratic formula.
The quadratic formula is given by:
y = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, the coefficients are:
a = 42
b = -29
c = -6
Plugging these values into the quadratic formula, we get:
y = (-(-29) ± √((-29)^2 - 4*42*(-6))) / (2*42)
Simplifying further:
y = (29 ± √(841 + 1008)) / 84
y = (29 ± √(1849)) / 84
y = (29 ± 43) / 84
Now, we have two possible solutions:
Solution 1:
y = (29 + 43) / 84
y = 72 / 84
y = 6 / 7
Solution 2:
y = (29 - 43) / 84
y = -14 / 84
y = -1 / 6
The exact solutions for the equation 42y^2 - 6 = 29y are y = 6/7 and y = -1/6.