Question

question
use the quadratic formula to solve. express your answer in simplest form.
11y² - 12y + 4 = 6y²
answer attempt 1 out of 2
additional solution no solution
y =
submit answer

Explanation:

Step1: Rearrange the equation

First, we need to rewrite the given equation \(11y^{2}-12y + 4=6y^{2}\) in the standard quadratic form \(ay^{2}+by + c = 0\). Subtract \(6y^{2}\) from both sides:
\(11y^{2}-6y^{2}-12y + 4=0\)
Simplify the \(y^{2}\) terms: \(5y^{2}-12y + 4 = 0\)
Here, \(a = 5\), \(b=- 12\), \(c = 4\).

Step2: Apply the quadratic formula

The quadratic formula is \(y=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). Substitute \(a = 5\), \(b=-12\), \(c = 4\) into the formula:
First, calculate the discriminant \(\Delta=b^{2}-4ac=(-12)^{2}-4\times5\times4\)
\(\Delta = 144 - 80=64\)
Then, \(y=\frac{-(-12)\pm\sqrt{64}}{2\times5}=\frac{12\pm8}{10}\)

Step3: Find the two solutions

For the plus sign: \(y=\frac{12 + 8}{10}=\frac{20}{10}=2\)
For the minus sign: \(y=\frac{12-8}{10}=\frac{4}{10}=\frac{2}{5}\)

Answer:

\(y = 2\) or \(y=\frac{2}{5}\)