Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x-6/x=-1
-
Equation cos(x)-1/2=0
-
Equation tg(x)=0
- Equation x^5-32=0
- Express {x} in terms of y where:
- -14*x+1*y=3
- -11*x+4*y=-8
- 16*x+7*y=8
- 17*x-11*y=2
- Graphing y =:
- x-6/x
- Integral of d{x}:
- x-6/x
-
-1
- Limit of the function:
-
x-6/x
- Sum of series:
-
-1
- Derivative of:
-
-1
-
Identical expressions
- x- six /x=- one
- x minus 6 divide by x equally minus 1
- x minus six divide by x equally minus one
- x-6 divide by x=-1
-
Similar expressions
- ((2*(x^2+6x+8)-(x^2-5x-6))/(x^2+3x+2))-41=0
- (-x-6)/(x-13)=-6
- (2*x-6)/(x-3)-(x^2-6*x+3)/(x-3)^2=0
- (x-6)/(x-9)=5
- x+6/x=-1
- x-6/x=+1
x-6/x=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$x - \frac{6}{x} = -1$$
Multiply the equation sides by the denominators:
and x
we get:
$$x \left(x - \frac{6}{x}\right) = - x$$
$$x^{2} - 6 = - x$$
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x^{2} - 6 = - x$$
to
$$x^{2} + x - 6 = 0$$
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
$$a = 1$$
$$b = 1$$
$$c = -6$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = -3$$
$$x - \frac{6}{x} = -1$$
Multiply the equation sides by the denominators:
and x
we get:
$$x \left(x - \frac{6}{x}\right) = - x$$
$$x^{2} - 6 = - x$$
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x^{2} - 6 = - x$$
to
$$x^{2} + x - 6 = 0$$
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
$$a = 1$$
$$b = 1$$
$$c = -6$$
, then
D = b^2 - 4 * a * c =
(1)^2 - 4 * (1) * (-6) = 25
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = -3$$
Sum and product of roots
[src]
sum
-3 + 2
$$-3 + 2$$
=
-1
$$-1$$
product
-3*2
$$- 6$$
=
-6
$$-6$$
-6
The graph