How do you solve y = 16x^2 + 40x + 25 using the quadratic formula?

Apr 29, 2016

The solution is
$x = - \frac{5}{4}$

Explanation:

$y = 16 {x}^{2} + 40 x + 25$

$16 {x}^{2} + 40 x + 25 = 0$

The equation is of the form color(blue)(ax^2+bx+c=0 where:

$a = 16 , b = 40 , c = 25$

The Discriminant is given by:

$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(40\right)}^{2} - \left(4 \cdot 16 \cdot 25\right)$

$= 1600 - 1600 = 0$

The solutions are normally found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

$x = \frac{\left(- 40\right) \pm \sqrt{0}}{2 \cdot 16} = \frac{- 40 \pm 0}{32}$

$x = - \frac{40}{32}$

$x = - \frac{5}{4}$