Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2=-74
-
Equation ctg(x/2)=√3
-
Equation 1/x=0
- Equation 3sin^2(3x)-2,5sin(6x)+1=0
- Express {x} in terms of y where:
- 9*x-8*y=6
- 15*x+15*y=16
- -4*x+18*y=-14
- 8*x+7*y=-13
- Graphing y =:
- x^2
- Derivative of:
-
x^2
- Integral of d{x}:
-
x^2
-
Identical expressions
- x^ two =- seventy-four
- x squared equally minus 74
- x to the power of two equally minus seventy minus four
- x2=-74
- x²=-74
- x to the power of 2=-74
-
Similar expressions
- x^2+4x-32=0
- 1-7(4+2x)=-9-4x
- 1-7*(4+2x)=-9-4x
- 3x^2=0
- 1-7*(4+2*x)=-9-4*x
- 5(2-5x)-7(4x-1)=6x-42
- 2*x^4-15*x^3+35*x^2-30x+8=0
- x^4-7x^2+12=0
- x^2=+74
x^2=-74 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
$$x^{2} = -74$$
to
$$x^{2} + 74 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = 74$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = \sqrt{74} i$$
$$x_{2} = - \sqrt{74} i$$
left part with negative sign.
The equation is transformed from
$$x^{2} = -74$$
to
$$x^{2} + 74 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = 74$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (74) = -296
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
$$x_{1} = \sqrt{74} i$$
$$x_{2} = - \sqrt{74} i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 74$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 74$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 74$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 74$$
Sum and product of roots
[src]
sum
____ ____ - I*\/ 74 + I*\/ 74
$$- \sqrt{74} i + \sqrt{74} i$$
=
0
$$0$$
product
____ ____ -I*\/ 74 *I*\/ 74
$$- \sqrt{74} i \sqrt{74} i$$
=
74
$$74$$
74
Rapid solution
[src]
____ x1 = -I*\/ 74
$$x_{1} = - \sqrt{74} i$$
____ x2 = I*\/ 74
$$x_{2} = \sqrt{74} i$$
x2 = sqrt(74)*i
The graph