Question

2. Solve the equation using the quadratic
formula.
-4x2 + 40x + 16 = 0
Page 1 of 2

Answer 1

The solution to given quadratic equation is x = -0.3851 or x = 10.3851

Solution:

Given equation is:

`-4x^2 + 40x + 16 = 0`

To find: solve by quadratic equation formula

`\text {For a quadratic equation } a x^(2)+b x+c=0, \text { where } a \\eq 0\\\\x=\frac{-b \pm \sqrt{b^(2)-4 a c}}{2 a}`

Using the above formula,

`\text{ For} -4x^2 + 40x + 16 = 0 \text{ we have } a = -4 ; b = 40 ; c = 16`

Substituting the values of a = -4 ; b = 40 ; c = 16 in above quadratic formula we get,

`\begin{aligned}&x=\frac{-40 \pm \sqrt{40^(2)-4(-4)(16)}}{2 *-4}\\\\&x=(-40 \pm √(1600+256))/(-8)\\\\&x=(-40 \pm 43.081)/(-8)\\\\&x=(-40+43.081)/(-8) \text { or } x=(-40-43.081)/(-8)\\\\&x=-0.3851 \text { or } x=10.3851\end{aligned}`

Thus the solution to given quadratic equation is x = - 0.3851 or x = 10.3851