# How do you solve the equation 4x^2=20x-25 by completing the square?

Apr 29, 2017

$\frac{5}{2}$

#### Explanation:

given,$4 {x}^{2} = 20 x - 25$

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

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

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

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

$\Rightarrow 2 x = 5$

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