Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 0,6-1,6(x-4)=3(7-0,4x)
-
Equation 4^(x-1/2)-6*2^(x-1)+3=0
-
Equation 8*x=16
-
Equation x^2=25x
- Express {x} in terms of y where:
- -2*x-17*y=-13
- -18*x-3*y=4
- -2*x+14*y=13
- 2*x-9*y=3
-
Identical expressions
- sixty-four *(x+y)/64x+8 zero y=0. ninety-six
- 64 multiply by (x plus y) divide by 64x plus 80y equally 0.96
- sixty minus four multiply by (x plus y) divide by 64x plus 8 zero y equally 0. ninety minus six
- 64(x+y)/64x+80y=0.96
- 64x+y/64x+80y=0.96
- 64*(x+y)/64x+80y=O.96
- 64*(x+y) divide by 64x+80y=0.96
-
Similar expressions
- 64*(x+y)/64x-80y=0.96
- 64*(x-y)/64x+80y=0.96
64*(x+y)/64x+80y=0.96 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
64*(x + y)*x 24
------------ + 80*y = --
64 25
$$\frac{64 x \left(x + y\right)}{64} + 80 y = \frac{24}{25}$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$\frac{64 x \left(x + y\right)}{64} + 80 y = \frac{24}{25}$$
to
$$\left(\frac{64 x \left(x + y\right)}{64} + 80 y\right) - \frac{24}{25} = 0$$
Expand the expression in the equation
$$\left(\frac{64 x \left(x + y\right)}{64} + 80 y\right) - \frac{24}{25} = 0$$
We get the quadratic equation
$$x^{2} + x y + 80 y - \frac{24}{25} = 0$$
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
$$a = 1$$
$$b = y$$
$$c = 80 y - \frac{24}{25}$$
, then
The equation has two roots.
or
$$x_{1} = - \frac{y}{2} + \frac{\sqrt{y^{2} - 320 y + \frac{96}{25}}}{2}$$
Simplify
$$x_{2} = - \frac{y}{2} - \frac{\sqrt{y^{2} - 320 y + \frac{96}{25}}}{2}$$
Simplify
left part with negative sign.
The equation is transformed from
$$\frac{64 x \left(x + y\right)}{64} + 80 y = \frac{24}{25}$$
to
$$\left(\frac{64 x \left(x + y\right)}{64} + 80 y\right) - \frac{24}{25} = 0$$
Expand the expression in the equation
$$\left(\frac{64 x \left(x + y\right)}{64} + 80 y\right) - \frac{24}{25} = 0$$
We get the quadratic equation
$$x^{2} + x y + 80 y - \frac{24}{25} = 0$$
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
$$a = 1$$
$$b = y$$
$$c = 80 y - \frac{24}{25}$$
, then
D = b^2 - 4 * a * c =
(y)^2 - 4 * (1) * (-24/25 + 80*y) = 96/25 + y^2 - 320*y
The equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{y}{2} + \frac{\sqrt{y^{2} - 320 y + \frac{96}{25}}}{2}$$
Simplify
$$x_{2} = - \frac{y}{2} - \frac{\sqrt{y^{2} - 320 y + \frac{96}{25}}}{2}$$
Simplify
The graph
Rapid solution
[src]
_____________________
/ 2
y \/ 96 - 8000*y + 25*y
x1 = - - - ------------------------
2 10
$$x_{1} = - \frac{y}{2} - \frac{\sqrt{25 y^{2} - 8000 y + 96}}{10}$$
_____________________
/ 2
y \/ 96 - 8000*y + 25*y
x2 = - - + ------------------------
2 10
$$x_{2} = - \frac{y}{2} + \frac{\sqrt{25 y^{2} - 8000 y + 96}}{10}$$
Sum and product of roots
[src]
sum
_____________________ _____________________
/ 2 / 2
y \/ 96 - 8000*y + 25*y y \/ 96 - 8000*y + 25*y
0 + - - - ------------------------ + - - + ------------------------
2 10 2 10
$$\left(- \frac{y}{2} + \frac{\sqrt{25 y^{2} - 8000 y + 96}}{10}\right) + \left(\left(- \frac{y}{2} - \frac{\sqrt{25 y^{2} - 8000 y + 96}}{10}\right) + 0\right)$$
=
-y
$$- y$$
product
/ _____________________\ / _____________________\ | / 2 | | / 2 | | y \/ 96 - 8000*y + 25*y | | y \/ 96 - 8000*y + 25*y | 1*|- - - ------------------------|*|- - + ------------------------| \ 2 10 / \ 2 10 /
$$1 \left(- \frac{y}{2} - \frac{\sqrt{25 y^{2} - 8000 y + 96}}{10}\right) \left(- \frac{y}{2} + \frac{\sqrt{25 y^{2} - 8000 y + 96}}{10}\right)$$
=
24 - -- + 80*y 25
$$80 y - \frac{24}{25}$$
-24/25 + 80*y