How do you solve 4x² - 20x + 25 = 0?

Jul 1, 2015

I would solve by factoring.

Explanation:

$4 {x}^{2} - 20 x + 25 = 0$

Look at $4 {x}^{2} - 20 x + 25$

the first term is a perfect square: $4 {x}^{2} = {\left(2 x\right)}^{2}$

the last term is a perfect square: $25 = {5}^{2}$

If we double the product f the things we squared, we get:

$2 \cdot \left(2 x\right) \left(5\right) = 20 x$, which is the absolute value of the middle term.

${\left(a x - b\right)}^{2} = {a}^{2} {x}^{2} - 2 a b x + {b}^{2}$, so we can factor:

$4 {x}^{2} - 20 x + 25 = {\left(2 x - 5\right)}^{2}$

With practice, there is no need to write the stuff up to this point, we can write:

$4 {x}^{2} - 20 x + 25 = 0$

${\left(2 x - 5\right)}^{2} = 0$

$2 x - 5 = 0$

$x = \frac{5}{2}$