Mister Exam

Other calculators


25*x^2=16

25*x^2=16 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     
25*x  = 16
$$25 x^{2} = 16$$
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
$$25 x^{2} = 16$$
to
$$25 x^{2} - 16 = 0$$
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
$$a = 25$$
$$b = 0$$
$$c = -16$$
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (25) * (-16) = 1600

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

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

or
$$x_{1} = \frac{4}{5}$$
$$x_{2} = - \frac{4}{5}$$
Vieta's Theorem
rewrite the equation
$$25 x^{2} = 16$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{16}{25} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{16}{25}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{16}{25}$$
The graph
Rapid solution [src]
x1 = -4/5
$$x_{1} = - \frac{4}{5}$$
x2 = 4/5
$$x_{2} = \frac{4}{5}$$
x2 = 4/5
Sum and product of roots [src]
sum
-4/5 + 4/5
$$- \frac{4}{5} + \frac{4}{5}$$
=
0
$$0$$
product
-4*4
----
5*5 
$$- \frac{16}{25}$$
=
-16 
----
 25 
$$- \frac{16}{25}$$
-16/25
Numerical answer [src]
x1 = 0.8
x2 = -0.8
x2 = -0.8
The graph
25*x^2=16 equation