Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation e^x=0
-
Equation 17x-8=20x+7
-
Equation 2*x^2+6*x+9=
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Equation -x=8
- Express {x} in terms of y where:
- 17*x+20*y=-12
- 17*x+16*y=7
- -5*x+6*y=19
- 18*x-14*y=-12
-
Identical expressions
- (x+ one)^ two *(five -x)+ fifty-four -(one +x)- nine (five -x)= zero
- (x plus 1) squared multiply by (5 minus x) plus 54 minus (1 plus x) minus 9(5 minus x) equally 0
- (x plus one) to the power of two multiply by (five minus x) plus fifty minus four minus (one plus x) minus nine (five minus x) equally zero
- (x+1)2*(5-x)+54-(1+x)-9(5-x)=0
- x+12*5-x+54-1+x-95-x=0
- (x+1)²*(5-x)+54-(1+x)-9(5-x)=0
- (x+1) to the power of 2*(5-x)+54-(1+x)-9(5-x)=0
- (x+1)^2(5-x)+54-(1+x)-9(5-x)=0
- (x+1)2(5-x)+54-(1+x)-9(5-x)=0
- x+125-x+54-1+x-95-x=0
- x+1^25-x+54-1+x-95-x=0
- (x+1)^2*(5-x)+54-(1+x)-9(5-x)=O
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Similar expressions
- (x+1)^2*(5-x)+54-(1+x)-9(5+x)=0
- (x-1)^2*(5-x)+54-(1+x)-9(5-x)=0
- (x+1)^2*(5-x)+54-(1-x)-9(5-x)=0
- (x+1)^2*(5-x)-54-(1+x)-9(5-x)=0
- (x+1)^2*(5+x)+54-(1+x)-9(5-x)=0
- (x+1)^2*(5-x)+54-(1+x)+9(5-x)=0
- (x+1)^2*(5-x)+54+(1+x)-9(5-x)=0
(x+1)^2*(5-x)+54-(1+x)-9(5-x)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 (x + 1) *(5 - x) + 54 + -1 - x - 9*(5 - x) = 0
$$- 9 \left(5 - x\right) + \left(\left(- x - 1\right) + \left(\left(5 - x\right) \left(x + 1\right)^{2} + 54\right)\right) = 0$$
Detail solution
Given the equation:
$$- 9 \left(5 - x\right) + \left(\left(- x - 1\right) + \left(\left(5 - x\right) \left(x + 1\right)^{2} + 54\right)\right) = 0$$
transform:
Take common factor from the equation
$$- \left(x + 1\right) \left(x^{2} - 4 x - 13\right) = 0$$
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
$$- x - 1 = 0$$
$$x^{2} - 4 x - 13 = 0$$
solve the resulting equation:
1.
$$- x - 1 = 0$$
Move free summands (without x)
from left part to right part, we given:
$$- x = 1$$
Divide both parts of the equation by -1
We get the answer: x1 = -1
2.
$$x^{2} - 4 x - 13 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{2} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{3} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -4$$
$$c = -13$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{2} = 2 + \sqrt{17}$$
$$x_{3} = 2 - \sqrt{17}$$
The final answer:
$$x_{1} = -1$$
$$x_{2} = 2 + \sqrt{17}$$
$$x_{3} = 2 - \sqrt{17}$$
$$- 9 \left(5 - x\right) + \left(\left(- x - 1\right) + \left(\left(5 - x\right) \left(x + 1\right)^{2} + 54\right)\right) = 0$$
transform:
Take common factor from the equation
$$- \left(x + 1\right) \left(x^{2} - 4 x - 13\right) = 0$$
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
$$- x - 1 = 0$$
$$x^{2} - 4 x - 13 = 0$$
solve the resulting equation:
1.
$$- x - 1 = 0$$
Move free summands (without x)
from left part to right part, we given:
$$- x = 1$$
Divide both parts of the equation by -1
x = 1 / (-1)
We get the answer: x1 = -1
2.
$$x^{2} - 4 x - 13 = 0$$
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:
$$x_{2} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{3} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -4$$
$$c = -13$$
, then
D = b^2 - 4 * a * c =
(-4)^2 - 4 * (1) * (-13) = 68
Because D > 0, then the equation has two roots.
x2 = (-b + sqrt(D)) / (2*a)
x3 = (-b - sqrt(D)) / (2*a)
or
$$x_{2} = 2 + \sqrt{17}$$
$$x_{3} = 2 - \sqrt{17}$$
The final answer:
$$x_{1} = -1$$
$$x_{2} = 2 + \sqrt{17}$$
$$x_{3} = 2 - \sqrt{17}$$
Rapid solution
[src]
x1 = -1
$$x_{1} = -1$$
____ x2 = 2 - \/ 17
$$x_{2} = 2 - \sqrt{17}$$
____ x3 = 2 + \/ 17
$$x_{3} = 2 + \sqrt{17}$$
x3 = 2 + sqrt(17)
Sum and product of roots
[src]
sum
____ ____ -1 + 2 - \/ 17 + 2 + \/ 17
$$\left(\left(2 - \sqrt{17}\right) - 1\right) + \left(2 + \sqrt{17}\right)$$
=
3
$$3$$
product
/ ____\ / ____\ -\2 - \/ 17 /*\2 + \/ 17 /
$$- (2 - \sqrt{17}) \left(2 + \sqrt{17}\right)$$
=
13
$$13$$
13