Question

question 7 of 10
find the solutions to the equation below.
check all that apply.
20x² - 26x + 8 = 0
a. x = 1/5
b. x = 2/3
c. x = 3/5
d. x = 1/2
e. x = 4/5
f. x = 1/3

Explanation:

Step1: Simplify the equation

Divide the entire equation $20x^{2}-26x + 8=0$ by 2 to get $10x^{2}-13x + 4 = 0$.

Step2: Use the quadratic - formula

For a quadratic equation $ax^{2}+bx + c = 0$ ($a = 10$, $b=-13$, $c = 4$), the quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. First, calculate the discriminant $\Delta=b^{2}-4ac=(-13)^{2}-4\times10\times4=169 - 160 = 9$.

Step3: Find the roots

$x=\frac{13\pm\sqrt{9}}{2\times10}=\frac{13\pm3}{20}$.
When we take the plus - sign: $x=\frac{13 + 3}{20}=\frac{16}{20}=\frac{4}{5}$.
When we take the minus - sign: $x=\frac{13-3}{20}=\frac{10}{20}=\frac{1}{2}$.

Answer:

D. $x=\frac{1}{2}$, E. $x=\frac{4}{5}$