Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 3^x=27
-
Equation x^2=12
-
Equation 12-x^2=11
-
Equation -sin(x)=0
- Express {x} in terms of y where:
- -5*x-6*y=-1
- -17*x-15*y=-17
- -2*x+7*y=-14
- -11*x-1*y=15
- Graphing y =:
- x^2
- Derivative of:
-
x^2
- 12
- Integral of d{x}:
-
x^2
-
12
- Limit of the function:
-
12
-
Identical expressions
- x^ two = twelve
- x squared equally 12
- x to the power of two equally twelve
- x2=12
- x²=12
- x to the power of 2=12
-
Similar expressions
- x^2-10*y+2x+y^2+26=0
- 6x^2-35x+50=0
- a^2-4*a*x+4*x^2-36=0
- 2x^2-2√2x-3=0
- 7x^2+8x+6=0
x^2=12 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
$$x^{2} = 12$$
to
$$x^{2} - 12 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -12$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2 \sqrt{3}$$
$$x_{2} = - 2 \sqrt{3}$$
left part with negative sign.
The equation is transformed from
$$x^{2} = 12$$
to
$$x^{2} - 12 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -12$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-12) = 48
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2 \sqrt{3}$$
$$x_{2} = - 2 \sqrt{3}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -12$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -12$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -12$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -12$$
Sum and product of roots
[src]
sum
___ ___ - 2*\/ 3 + 2*\/ 3
$$- 2 \sqrt{3} + 2 \sqrt{3}$$
=
0
$$0$$
product
___ ___ -2*\/ 3 *2*\/ 3
$$- 2 \sqrt{3} \cdot 2 \sqrt{3}$$
=
-12
$$-12$$
-12
Rapid solution
[src]
___ x1 = -2*\/ 3
$$x_{1} = - 2 \sqrt{3}$$
___ x2 = 2*\/ 3
$$x_{2} = 2 \sqrt{3}$$
x2 = 2*sqrt(3)
The graph