Question

use the quadratic formula to solve the equation $25x^2 - 50x + 36 = 0$. enter multiple answers as a list separated by commas. example: $2 + 2i, 2 - 2i$ question help: video 1 video 2

Explanation:

Step1: Identify a, b, c values

For $25x^2 -50x +36=0$, $a=25$, $b=-50$, $c=36$

Step2: Write quadratic formula

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Step3: Calculate discriminant

$$b^2-4ac=(-50)^2-4(25)(36)=2500-3600=-1100$$

Step4: Simplify square root

$\sqrt{-1100}=\sqrt{100\times(-11)}=10i\sqrt{11}$

Step5: Substitute into formula

$$x=\frac{50\pm10i\sqrt{11}}{2\times25}=\frac{50\pm10i\sqrt{11}}{50}$$

Step6: Simplify the fraction

$$x=1\pm\frac{\sqrt{11}}{5}i$$

Answer:

$1+\frac{\sqrt{11}}{5}i, 1-\frac{\sqrt{11}}{5}i$