Mister Exam
Other calculators
-
How to use it?
- Equation:
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Equation 2+3x=-2x-13
-
Equation cos(x)=-(1/2)
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Equation sin(x/3)=-1/2
-
Equation |x^2-1|-|x-3|=7
- Express {x} in terms of y where:
- -14*x-16*y=14
- 16*x-17*y=-9
- -14*x-3*y=-5
- -16*x-20*y=6
- Integral of d{x}:
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2x^2
- Derivative of:
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2x^2
- Canonical form:
- 2x^2
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Identical expressions
- twenty-seven (one /3x- one)(one /9x^ two + one /3x+ one)-x(x- one)(x+ one)= two x^2
- 27(1 divide by 3x minus 1)(1 divide by 9x squared plus 1 divide by 3x plus 1) minus x(x minus 1)(x plus 1) equally 2x squared
- twenty minus seven (one divide by 3x minus one)(one divide by 9x to the power of two plus one divide by 3x plus one) minus x(x minus one)(x plus one) equally two x squared
- 27(1/3x-1)(1/9x2+1/3x+1)-x(x-1)(x+1)=2x2
- 271/3x-11/9x2+1/3x+1-xx-1x+1=2x2
- 27(1/3x-1)(1/9x²+1/3x+1)-x(x-1)(x+1)=2x²
- 27(1/3x-1)(1/9x to the power of 2+1/3x+1)-x(x-1)(x+1)=2x to the power of 2
- 271/3x-11/9x^2+1/3x+1-xx-1x+1=2x^2
- 27(1 divide by 3x-1)(1 divide by 9x^2+1 divide by 3x+1)-x(x-1)(x+1)=2x^2
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Similar expressions
- 27(1/3x-1)(1/9x^2+1/3x+1)-x(x-1)(x-1)=2x^2
- (sqrt(x)-3)*(2*x^2+3*x-5)=0
- 1/2x^2-32=0
- sqrt(16-x^2)*(x^2-3*x-10)=0
- 27(1/3x+1)(1/9x^2+1/3x+1)-x(x-1)(x+1)=2x^2
- 27(1/3x-1)(1/9x^2+1/3x+1)+x(x-1)(x+1)=2x^2
- 27(1/3x-1)(1/9x^2+1/3x-1)-x(x-1)(x+1)=2x^2
- -2*x+4*x+5=2*x^2-7*x+2*x-3
- 27(1/3x-1)(1/9x^2-1/3x+1)-x(x-1)(x+1)=2x^2
- 2x^2-10x=0
- 27(1/3x-1)(1/9x^2+1/3x+1)-x(x+1)(x+1)=2x^2
27(1/3x-1)(1/9x^2+1/3x+1)-x(x-1)(x+1)=2x^2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ 2 \ /x \ |x x | 2 27*|- - 1|*|-- + - + 1| - x*(x - 1)*(x + 1) = 2*x \3 / \9 3 /
$$- x \left(x - 1\right) \left(x + 1\right) + 27 \left(\frac{x}{3} - 1\right) \left(\left(\frac{x^{2}}{9} + \frac{x}{3}\right) + 1\right) = 2 x^{2}$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$- x \left(x - 1\right) \left(x + 1\right) + 27 \left(\frac{x}{3} - 1\right) \left(\left(\frac{x^{2}}{9} + \frac{x}{3}\right) + 1\right) = 2 x^{2}$$
to
$$- 2 x^{2} + \left(- x \left(x - 1\right) \left(x + 1\right) + 27 \left(\frac{x}{3} - 1\right) \left(\left(\frac{x^{2}}{9} + \frac{x}{3}\right) + 1\right)\right) = 0$$
Expand the expression in the equation
$$- 2 x^{2} + \left(- x \left(x - 1\right) \left(x + 1\right) + 27 \left(\frac{x}{3} - 1\right) \left(\left(\frac{x^{2}}{9} + \frac{x}{3}\right) + 1\right)\right) = 0$$
We get the quadratic equation
$$- 2 x^{2} + x - 27 = 0$$
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
$$a = -2$$
$$b = 1$$
$$c = -27$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = \frac{1}{4} - \frac{\sqrt{215} i}{4}$$
$$x_{2} = \frac{1}{4} + \frac{\sqrt{215} i}{4}$$
left part with negative sign.
The equation is transformed from
$$- x \left(x - 1\right) \left(x + 1\right) + 27 \left(\frac{x}{3} - 1\right) \left(\left(\frac{x^{2}}{9} + \frac{x}{3}\right) + 1\right) = 2 x^{2}$$
to
$$- 2 x^{2} + \left(- x \left(x - 1\right) \left(x + 1\right) + 27 \left(\frac{x}{3} - 1\right) \left(\left(\frac{x^{2}}{9} + \frac{x}{3}\right) + 1\right)\right) = 0$$
Expand the expression in the equation
$$- 2 x^{2} + \left(- x \left(x - 1\right) \left(x + 1\right) + 27 \left(\frac{x}{3} - 1\right) \left(\left(\frac{x^{2}}{9} + \frac{x}{3}\right) + 1\right)\right) = 0$$
We get the quadratic equation
$$- 2 x^{2} + x - 27 = 0$$
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
$$a = -2$$
$$b = 1$$
$$c = -27$$
, then
D = b^2 - 4 * a * c =
(1)^2 - 4 * (-2) * (-27) = -215
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
$$x_{1} = \frac{1}{4} - \frac{\sqrt{215} i}{4}$$
$$x_{2} = \frac{1}{4} + \frac{\sqrt{215} i}{4}$$
Sum and product of roots
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sum
_____ _____ 1 I*\/ 215 1 I*\/ 215 - - --------- + - + --------- 4 4 4 4
$$\left(\frac{1}{4} - \frac{\sqrt{215} i}{4}\right) + \left(\frac{1}{4} + \frac{\sqrt{215} i}{4}\right)$$
=
1/2
$$\frac{1}{2}$$
product
/ _____\ / _____\ |1 I*\/ 215 | |1 I*\/ 215 | |- - ---------|*|- + ---------| \4 4 / \4 4 /
$$\left(\frac{1}{4} - \frac{\sqrt{215} i}{4}\right) \left(\frac{1}{4} + \frac{\sqrt{215} i}{4}\right)$$
=
27/2
$$\frac{27}{2}$$
27/2
Rapid solution
[src]
_____
1 I*\/ 215
x1 = - - ---------
4 4
$$x_{1} = \frac{1}{4} - \frac{\sqrt{215} i}{4}$$
_____
1 I*\/ 215
x2 = - + ---------
4 4
$$x_{2} = \frac{1}{4} + \frac{\sqrt{215} i}{4}$$
x2 = 1/4 + sqrt(215)*i/4
Numerical answer
[src]
x1 = 0.25 - 3.66571957465379*i
x2 = 0.25 + 3.66571957465379*i
x2 = 0.25 + 3.66571957465379*i