# How do you solve 2x^2 - 250x + 5000 = 0?

Mar 31, 2018

25,100

#### Explanation:

$2 {x}^{2} - 250 x + 5000 = 0$
$\Rightarrow 2 \left({x}^{2} - 125 x + 2500\right) = 0$
$\Rightarrow {x}^{2} - 125 x + 2500 = 0$
$\Rightarrow {x}^{2} - 25 x - 100 x + 2500 = 0$
$\Rightarrow x \left(x - 25\right) - 100 \left(x - 25\right) = 0$
$\Rightarrow \left(x - 25\right) \left(x - 100\right) = 0$
$\Rightarrow \left(x - 25\right) = 0 , \left(x - 100\right) = 0$
rArr x = 25 & 100

Mar 31, 2018

$x = 25 \text{ or } x = 100$

#### Explanation:

$\text{take out a "color(blue)"common factor } 2$

$\Rightarrow 2 \left({x}^{2} - 125 x + 2500\right) = 0$

$\text{the factors of + 2500 which sum to - 125 are - 25 and - 100}$

$\Rightarrow 2 \left(x - 25\right) \left(x - 100\right) = 0$

$\text{equate each factor to zero and solve for x}$

$x - 25 = 0 \Rightarrow x = 25$

$x - 100 = 0 \Rightarrow x = 100$