Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2-4x+6=0
-
Equation 5*x=12
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Equation 3*x=12
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Equation 8=3x-x
- Express {x} in terms of y where:
- 11*x-20*y=-14
- -16*x+2*y=16
- 15*x+13*y=-3
- -7*x+12*y=14
-
Identical expressions
- √(five x- one /5)= three
- √(5x minus 1 divide by 5) equally 3
- √(five x minus one divide by 5) equally three
- √5x-1/5=3
- √(5x-1 divide by 5)=3
-
Similar expressions
- √(5x+1/5)=3
√(5x-1/5)=3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{5 x - \frac{1}{5}} = 3$$
Because equation degree is equal to = 1/2 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 2-th degree:
We get:
$$\left(\sqrt{5 x - \frac{1}{5}}\right)^{2} = 3^{2}$$
or
$$5 x - \frac{1}{5} = 9$$
Move free summands (without x)
from left part to right part, we given:
$$5 x = \frac{46}{5}$$
Divide both parts of the equation by 5
We get the answer: x = 46/25
The final answer:
$$x_{1} = \frac{46}{25}$$
$$\sqrt{5 x - \frac{1}{5}} = 3$$
Because equation degree is equal to = 1/2 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 2-th degree:
We get:
$$\left(\sqrt{5 x - \frac{1}{5}}\right)^{2} = 3^{2}$$
or
$$5 x - \frac{1}{5} = 9$$
Move free summands (without x)
from left part to right part, we given:
$$5 x = \frac{46}{5}$$
Divide both parts of the equation by 5
x = 46/5 / (5)
We get the answer: x = 46/25
The final answer:
$$x_{1} = \frac{46}{25}$$
Sum and product of roots
[src]
sum
46 -- 25
$$\frac{46}{25}$$
=
46 -- 25
$$\frac{46}{25}$$
product
46 -- 25
$$\frac{46}{25}$$
=
46 -- 25
$$\frac{46}{25}$$
46/25
Numerical answer
[src]
x1 = 1.84
x2 = 1.84 + 4.00742067749094e-17*i
x3 = 1.84 + 5.98077758579102e-15*i
x4 = 1.84000000000016 + 5.20136669345324e-13*i
x4 = 1.84000000000016 + 5.20136669345324e-13*i