Mister Exam

Other calculators

x^2-8x-84=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  - 8*x - 84 = 0
$$\left(x^{2} - 8 x\right) - 84 = 0$$
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
$$a = 1$$
$$b = -8$$
$$c = -84$$
, then
D = b^2 - 4 * a * c = 

(-8)^2 - 4 * (1) * (-84) = 400

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

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

or
$$x_{1} = 14$$
$$x_{2} = -6$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = -84$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = -84$$
Sum and product of roots [src]
sum
-6 + 14
$$-6 + 14$$
=
8
$$8$$
product
-6*14
$$- 84$$
=
-84
$$-84$$
-84
Rapid solution [src]
x1 = -6
$$x_{1} = -6$$
x2 = 14
$$x_{2} = 14$$
x2 = 14
Numerical answer [src]
x1 = 14.0
x2 = -6.0
x2 = -6.0