Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x-4)/x=(2*x+10)/(x+4)
-
Equation 9*x^2-1=0
-
Equation 2*sin(x)*cos(x)=0
-
Equation 3x-2=7x+6
- Express {x} in terms of y where:
- -1*x+1*y=-13
- 9*x-1*y=-10
- -19*x+20*y=-11
- -10*x+4*y=-7
-
Identical expressions
- x^ two + two *x+ two hundred and two / five thousand = zero
- x squared plus 2 multiply by x plus 202 divide by 5000 equally 0
- x to the power of two plus two multiply by x plus two hundred and two divide by five thousand equally zero
- x2+2*x+202/5000=0
- x²+2*x+202/5000=0
- x to the power of 2+2*x+202/5000=0
- x^2+2x+202/5000=0
- x2+2x+202/5000=0
- x^2+2*x+202/5000=O
- x^2+2*x+202 divide by 5000=0
-
Similar expressions
- x^2+2*x-202/5000=0
- x^2-2*x+202/5000=0
x^2+2*x+202/5000=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 101
x + 2*x + ---- = 0
2500
$$\left(x^{2} + 2 x\right) + \frac{101}{2500} = 0$$
Detail solution
This equation is of the form
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
$$a = 1$$
$$b = 2$$
$$c = \frac{101}{2500}$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -1 + \frac{\sqrt{2399}}{50}$$
$$x_{2} = -1 - \frac{\sqrt{2399}}{50}$$
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
$$a = 1$$
$$b = 2$$
$$c = \frac{101}{2500}$$
, then
D = b^2 - 4 * a * c =
(2)^2 - 4 * (1) * (101/2500) = 2399/625
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -1 + \frac{\sqrt{2399}}{50}$$
$$x_{2} = -1 - \frac{\sqrt{2399}}{50}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = \frac{101}{2500}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -2$$
$$x_{1} x_{2} = \frac{101}{2500}$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = \frac{101}{2500}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -2$$
$$x_{1} x_{2} = \frac{101}{2500}$$
Sum and product of roots
[src]
sum
______ ______
\/ 2399 \/ 2399
-1 - -------- + -1 + --------
50 50
$$\left(-1 - \frac{\sqrt{2399}}{50}\right) + \left(-1 + \frac{\sqrt{2399}}{50}\right)$$
=
-2
$$-2$$
product
/ ______\ / ______\ | \/ 2399 | | \/ 2399 | |-1 - --------|*|-1 + --------| \ 50 / \ 50 /
$$\left(-1 - \frac{\sqrt{2399}}{50}\right) \left(-1 + \frac{\sqrt{2399}}{50}\right)$$
=
101 ---- 2500
$$\frac{101}{2500}$$
101/2500
Rapid solution
[src]
______
\/ 2399
x1 = -1 - --------
50
$$x_{1} = -1 - \frac{\sqrt{2399}}{50}$$
______
\/ 2399
x2 = -1 + --------
50
$$x_{2} = -1 + \frac{\sqrt{2399}}{50}$$
x2 = -1 + sqrt(2399)/50