Question

question 8 of 10 step 1 of 1 solve the following quadratic equation using the quadratic formula. separate multiple answers with a comma if necessary. \\(-3y^2 - 3y + 1 = 0\\)

Explanation:

Step1: Identify coefficients

For $-3y^2 - 3y + 1 = 0$, $a=-3$, $b=-3$, $c=1$

Step2: Recall quadratic formula

Quadratic formula: $y=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step3: Compute discriminant

$\Delta = b^2-4ac = (-3)^2 - 4(-3)(1) = 9 + 12 = 21$

Step4: Substitute into formula

$y=\frac{-(-3)\pm\sqrt{21}}{2(-3)} = \frac{3\pm\sqrt{21}}{-6}$

Step5: Simplify expressions

$y=\frac{-3+\sqrt{21}}{6}$, $y=\frac{-3-\sqrt{21}}{6}$

Answer:

$y=\frac{-3+\sqrt{21}}{6}$, $y=\frac{-3-\sqrt{21}}{6}$