Bartlett Henry
01/22/2023 · Senior High School
\( \left\{\begin{array}{l}6y^{2}+9y-2 \\y+3\end{array}\right. \)
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Step-by-step Solution
It looks like you have a system of expressions or equations. However, it's not clear what you would like to do with them.
If you want to solve the equation \( 6y^2 + 9y - 2 = 0 \) or simplify the expression \( y + 3 \), please specify.
If you want to solve the quadratic equation \( 6y^2 + 9y - 2 = 0 \), we can use the quadratic formula:
\[
y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
where \( a = 6 \), \( b = 9 \), and \( c = -2 \).
Let's calculate the discriminant:
\[
b^2 - 4ac = 9^2 - 4 \cdot 6 \cdot (-2) = 81 + 48 = 129
\]
Now, we can find the roots:
\[
y = \frac{-9 \pm \sqrt{129}}{2 \cdot 6} = \frac{-9 \pm \sqrt{129}}{12}
\]
This gives us the two solutions for \( y \):
\[
y_1 = \frac{-9 + \sqrt{129}}{12}, \quad y_2 = \frac{-9 - \sqrt{129}}{12}
\]
If you need further assistance or a different operation, please let me know!
Quick Answer
To solve the quadratic equation \( 6y^2 + 9y - 2 = 0 \), use the quadratic formula to find the roots \( y_1 = \frac{-9 + \sqrt{129}}{12} \) and \( y_2 = \frac{-9 - \sqrt{129}}{12} \).
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