Respuesta :
The solution to given quadratic equation is x = -0.3851 or x = 10.3851
Solution:
Given equation is:
[tex]-4x^2 + 40x + 16 = 0[/tex]
To find: solve by quadratic equation formula
[tex]\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
Using the above formula,
[tex]\text{ For} -4x^2 + 40x + 16 = 0 \text{ we have } a = -4 ; b = 40 ; c = 16[/tex]
Substituting the values of a = -4 ; b = 40 ; c = 16 in above quadratic formula we get,
[tex]\begin{aligned}&x=\frac{-40 \pm \sqrt{40^{2}-4(-4)(16)}}{2 \times-4}\\\\&x=\frac{-40 \pm \sqrt{1600+256}}{-8}\\\\&x=\frac{-40 \pm 43.081}{-8}\\\\&x=\frac{-40+43.081}{-8} \text { or } x=\frac{-40-43.081}{-8}\\\\&x=-0.3851 \text { or } x=10.3851\end{aligned}[/tex]
Thus the solution to given quadratic equation is x = - 0.3851 or x = 10.3851
