Question

solve for w.
9w² - 20w + 4 = 0
write each solution as an integer, proper fraction, or improper fraction in simplest form.
if there are multiple solutions, separate them with commas.
w =

Explanation:

Step1: Identify coefficients

For the quadratic equation $9w^{2}-20w + 4=0$, where $a = 9$, $b=-20$, $c = 4$.

Step2: Use quadratic formula

The quadratic formula is $w=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute the values: $w=\frac{-(-20)\pm\sqrt{(-20)^{2}-4\times9\times4}}{2\times9}=\frac{20\pm\sqrt{400 - 144}}{18}=\frac{20\pm\sqrt{256}}{18}$.

Step3: Simplify square - root and solve

Since $\sqrt{256}=16$, then $w=\frac{20\pm16}{18}$.
For the plus - sign: $w_1=\frac{20 + 16}{18}=\frac{36}{18}=2$.
For the minus - sign: $w_2=\frac{20-16}{18}=\frac{4}{18}=\frac{2}{9}$.

Answer:

$2,\frac{2}{9}$