Mister Exam

Other calculators

x^2-2*x-80=0 equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src]
 2               
x  - 2*x - 80 = 0
$$\left(x^{2} - 2 x\right) - 80 = 0$$
Detail solution
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -2$$
$$c = -80$$
, then
D = b^2 - 4 * a * c = 

(-2)^2 - 4 * (1) * (-80) = 324

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
$$x_{1} = 10$$
$$x_{2} = -8$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -80$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -80$$
Sum and product of roots [src]
sum
-8 + 10
$$-8 + 10$$
=
2
$$2$$
product
-8*10
$$- 80$$
=
-80
$$-80$$
-80
Rapid solution [src]
x1 = -8
$$x_{1} = -8$$
x2 = 10
$$x_{2} = 10$$
x2 = 10
Numerical answer [src]
x1 = 10.0
x2 = -8.0
x2 = -8.0