Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x=x/2+1
-
Equation x^2=6
-
Equation (x+10)^2=(x-9)^2
-
Equation (7-x)^2=(x+16)^2
- Express {x} in terms of y where:
- -11*x+4*y=-8
- 17*x-11*y=2
- -14*x+1*y=3
- 1*x+19*y=-10
- Graphing y =:
- x^2
- Limit of the function:
-
x^2
- Derivative of:
-
x^2
-
Identical expressions
- x^ two = six
- x squared equally 6
- x to the power of two equally six
- x2=6
- x²=6
- x to the power of 2=6
-
Similar expressions
- (x-2)^2+(x-3)^2=2x^2
- ((65(cosx)^2)+63cosx)/(63(tgx)-16)=0
- x(x^2+6x+9)=4(x+3)
- x^2-3=0
x^2=6 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x^{2} = 6$$
to
$$x^{2} - 6 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -6$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{6}$$
$$x_{2} = - \sqrt{6}$$
left part with negative sign.
The equation is transformed from
$$x^{2} = 6$$
to
$$x^{2} - 6 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -6$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-6) = 24
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{6}$$
$$x_{2} = - \sqrt{6}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -6$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -6$$
Rapid solution
[src]
___ x1 = -\/ 6
$$x_{1} = - \sqrt{6}$$
___ x2 = \/ 6
$$x_{2} = \sqrt{6}$$
x2 = sqrt(6)
Sum and product of roots
[src]
sum
___ ___ - \/ 6 + \/ 6
$$- \sqrt{6} + \sqrt{6}$$
=
0
$$0$$
product
___ ___ -\/ 6 *\/ 6
$$- \sqrt{6} \sqrt{6}$$
=
-6
$$-6$$
-6
The graph