Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x+2)^2=(1-x)^2
-
Equation 2*cos(x)+1=0
-
Equation (-5*x-3)*(2*x-1)=0
-
Equation x^2-8x+15=0
- Express {x} in terms of y where:
- 7*x+13*y=-13
- 7*x+19*y=12
- 1*x+20*y=-17
- 14*x-16*y=-3
- Graphing y =:
- x^2
- Limit of the function:
-
x^2
- Derivative of:
-
x^2
-
-2
- Integral of d{x}:
-
-2
- Sum of series:
-
-2
-
Identical expressions
- x^ two =- two
- x squared equally minus 2
- x to the power of two equally minus two
- x2=-2
- x²=-2
- x to the power of 2=-2
-
Similar expressions
- 1/2x^2-32=0
- 12x=-36+3x^2
- x^2=+2
- (x^2-1)/x=0
- 3-3*x^2=0
x^2=-2 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
$$x^{2} = -2$$
to
$$x^{2} + 2 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = 2$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = \sqrt{2} i$$
Simplify
$$x_{2} = - \sqrt{2} i$$
Simplify
left part with negative sign.
The equation is transformed from
$$x^{2} = -2$$
to
$$x^{2} + 2 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = 2$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (2) = -8
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{2} i$$
Simplify
$$x_{2} = - \sqrt{2} i$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 2$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 2$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 2$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 2$$
Sum and product of roots
[src]
sum
___ ___ 0 - I*\/ 2 + I*\/ 2
$$\left(0 - \sqrt{2} i\right) + \sqrt{2} i$$
=
0
$$0$$
product
___ ___ 1*-I*\/ 2 *I*\/ 2
$$\sqrt{2} i 1 \left(- \sqrt{2} i\right)$$
=
2
$$2$$
2
Rapid solution
[src]
___ x1 = -I*\/ 2
$$x_{1} = - \sqrt{2} i$$
___ x2 = I*\/ 2
$$x_{2} = \sqrt{2} i$$
The graph