Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation cos(x)=(-1/2)
-
Equation sin(x-1)=0
-
Equation sin(x)=-3/2
-
Equation 5x-25+2x²=17+13x
- Express {x} in terms of y where:
- 12*10^(-30)-0,1884*10^12*x^2-y(0,3768*10^12*x+1,183152*10^12*x^3)+y^2(2,760688*10^24*x^2)=0=0
- (x^2+y^2)×(x+y-3)=2xy
- lnx^y=ln1
- sqrt(1-x)^2+(4-y)^2=0
- Integral of d{x}:
-
-3x^2
- Derivative of:
-
-3x^2
- Graphing y =:
- -3x^2
-
Identical expressions
- four (x+ one)(x+ two)(x+ three)(x+ six)=-3x^ two
- 4(x plus 1)(x plus 2)(x plus 3)(x plus 6) equally minus 3x squared
- four (x plus one)(x plus two)(x plus three)(x plus six) equally minus 3x to the power of two
- 4(x+1)(x+2)(x+3)(x+6)=-3x2
- 4x+1x+2x+3x+6=-3x2
- 4(x+1)(x+2)(x+3)(x+6)=-3x²
- 4(x+1)(x+2)(x+3)(x+6)=-3x to the power of 2
- 4x+1x+2x+3x+6=-3x^2
-
Similar expressions
- 4(x+1)(x+2)(x-3)(x+6)=-3x^2
- 4(x-1)(x+2)(x+3)(x+6)=-3x^2
- 4(x+1)(x-2)(x+3)(x+6)=-3x^2
- 4(x+1)(x+2)(x+3)(x+6)=+3x^2
- 4(x+1)(x+2)(x+3)(x-6)=-3x^2
4(x+1)(x+2)(x+3)(x+6)=-3x^2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
2 4*(x + 1)*(x + 2)*(x + 3)*(x + 6) = -3*x
$$4 \left(x + 1\right) \left(x + 2\right) \left(x + 3\right) \left(x + 6\right) = - 3 x^{2}$$
Detail solution
Given the equation:
$$4 \left(x + 1\right) \left(x + 2\right) \left(x + 3\right) \left(x + 6\right) = - 3 x^{2}$$
transform:
Take common factor from the equation
$$\left(x + 4\right) \left(2 x + 3\right) \left(2 x^{2} + 13 x + 12\right) = 0$$
Because the right side of the equation is zero, then the solution of the equation is exists if at least one of the multipliers in the left side of the equation equal to zero.
We get the equations
$$x + 4 = 0$$
$$2 x + 3 = 0$$
$$2 x^{2} + 13 x + 12 = 0$$
solve the resulting equation:
1.
$$x + 4 = 0$$
Move free summands (without x)
from left part to right part, we given:
$$x = -4$$
We get the answer: x1 = -4
2.
$$2 x + 3 = 0$$
Move free summands (without x)
from left part to right part, we given:
$$2 x = -3$$
Divide both parts of the equation by 2
We get the answer: x2 = -3/2
3.
$$2 x^{2} + 13 x + 12 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{3} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{4} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 2$$
$$b = 13$$
$$c = 12$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{3} = - \frac{13}{4} + \frac{\sqrt{73}}{4}$$
$$x_{4} = - \frac{13}{4} - \frac{\sqrt{73}}{4}$$
The final answer:
$$x_{1} = -4$$
$$x_{2} = - \frac{3}{2}$$
$$x_{3} = - \frac{13}{4} + \frac{\sqrt{73}}{4}$$
$$x_{4} = - \frac{13}{4} - \frac{\sqrt{73}}{4}$$
$$4 \left(x + 1\right) \left(x + 2\right) \left(x + 3\right) \left(x + 6\right) = - 3 x^{2}$$
transform:
Take common factor from the equation
$$\left(x + 4\right) \left(2 x + 3\right) \left(2 x^{2} + 13 x + 12\right) = 0$$
Because the right side of the equation is zero, then the solution of the equation is exists if at least one of the multipliers in the left side of the equation equal to zero.
We get the equations
$$x + 4 = 0$$
$$2 x + 3 = 0$$
$$2 x^{2} + 13 x + 12 = 0$$
solve the resulting equation:
1.
$$x + 4 = 0$$
Move free summands (without x)
from left part to right part, we given:
$$x = -4$$
We get the answer: x1 = -4
2.
$$2 x + 3 = 0$$
Move free summands (without x)
from left part to right part, we given:
$$2 x = -3$$
Divide both parts of the equation by 2
x = -3 / (2)
We get the answer: x2 = -3/2
3.
$$2 x^{2} + 13 x + 12 = 0$$
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:
$$x_{3} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{4} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 2$$
$$b = 13$$
$$c = 12$$
, then
D = b^2 - 4 * a * c =
(13)^2 - 4 * (2) * (12) = 73
Because D > 0, then the equation has two roots.
x3 = (-b + sqrt(D)) / (2*a)
x4 = (-b - sqrt(D)) / (2*a)
or
$$x_{3} = - \frac{13}{4} + \frac{\sqrt{73}}{4}$$
$$x_{4} = - \frac{13}{4} - \frac{\sqrt{73}}{4}$$
The final answer:
$$x_{1} = -4$$
$$x_{2} = - \frac{3}{2}$$
$$x_{3} = - \frac{13}{4} + \frac{\sqrt{73}}{4}$$
$$x_{4} = - \frac{13}{4} - \frac{\sqrt{73}}{4}$$
Rapid solution
[src]
x1 = -4
$$x_{1} = -4$$
x2 = -3/2
$$x_{2} = - \frac{3}{2}$$
____
13 \/ 73
x3 = - -- - ------
4 4
$$x_{3} = - \frac{13}{4} - \frac{\sqrt{73}}{4}$$
____
13 \/ 73
x4 = - -- + ------
4 4
$$x_{4} = - \frac{13}{4} + \frac{\sqrt{73}}{4}$$
x4 = -13/4 + sqrt(73)/4
Sum and product of roots
[src]
sum
____ ____
13 \/ 73 13 \/ 73
-4 - 3/2 + - -- - ------ + - -- + ------
4 4 4 4
$$\left(\left(-4 - \frac{3}{2}\right) + \left(- \frac{13}{4} - \frac{\sqrt{73}}{4}\right)\right) + \left(- \frac{13}{4} + \frac{\sqrt{73}}{4}\right)$$
=
-12
$$-12$$
product
/ ____\ / ____\ -4*(-3) | 13 \/ 73 | | 13 \/ 73 | -------*|- -- - ------|*|- -- + ------| 2 \ 4 4 / \ 4 4 /
$$- -6 \left(- \frac{13}{4} - \frac{\sqrt{73}}{4}\right) \left(- \frac{13}{4} + \frac{\sqrt{73}}{4}\right)$$
=
36
$$36$$
36
Numerical answer
[src]
x1 = -1.5
x2 = -4.0
x3 = -1.11399906367062
x4 = -5.38600093632938
x4 = -5.38600093632938