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- Equation:
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Equation (2*x-6)^2-4*x^2=0
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Equation x^3+9*x^2+27*x+27=0
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- Express {x} in terms of y where:
- -20*x+6*y=-12
- -11*x+16*y=-5
- -12*x-9*y=-3
- -6*x-2*y=7
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Identical expressions
- two million, one hundred and sixty thousand *x/(one + two . five *x)= two million, thirty thousand, four hundred and seventy-seven . thirty-two
- 2160000 multiply by x divide by (1 plus 2.5 multiply by x) equally 2030477.32
- two million, one hundred and sixty thousand multiply by x divide by (one plus two . five multiply by x) equally two million, thirty thousand, four hundred and seventy minus seven . thirty minus two
- 2160000x/(1+2.5x)=2030477.32
- 2160000x/1+2.5x=2030477.32
- 2160000*x divide by (1+2.5*x)=2030477.32
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Similar expressions
- 2160000*x/(1-2.5*x)=2030477.32
2160000*x/(1+2.5*x)=2030477.32 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2160000*x 50761933
--------- = --------
5*x 25
1 + ---
2
$$\frac{2160000 x}{\frac{5 x}{2} + 1} = \frac{50761933}{25}$$
Detail solution
Given the equation:
$$\frac{2160000 x}{\frac{5 x}{2} + 1} = \frac{50761933}{25}$$
Multiply the equation sides by the denominator 1 + 5*x/2
we get:
$$\frac{4320000 x \left(\frac{5 x}{2} + 1\right)}{5 x + 2} = \frac{50761933 x}{10} + \frac{50761933}{25}$$
Expand brackets in the left part
Looking for similar summands in the left part:
Move the summands with the unknown x
from the right part to the left part:
$$\frac{4320000 x \left(\frac{5 x}{2} + 1\right)}{5 x + 2} - \frac{50761933 x}{10} = \frac{50761933}{25}$$
Divide both parts of the equation by (-50761933*x/10 + 4320000*x*(1 + 5*x/2)/(2 + 5*x))/x
We get the answer: x = -101523866/145809665
$$\frac{2160000 x}{\frac{5 x}{2} + 1} = \frac{50761933}{25}$$
Multiply the equation sides by the denominator 1 + 5*x/2
we get:
$$\frac{4320000 x \left(\frac{5 x}{2} + 1\right)}{5 x + 2} = \frac{50761933 x}{10} + \frac{50761933}{25}$$
Expand brackets in the left part
4320000*x1+5*x/22+5*x = 50761933/25 + 50761933*x/10
Looking for similar summands in the left part:
4320000*x*(1 + 5*x/2)/(2 + 5*x) = 50761933/25 + 50761933*x/10
Move the summands with the unknown x
from the right part to the left part:
$$\frac{4320000 x \left(\frac{5 x}{2} + 1\right)}{5 x + 2} - \frac{50761933 x}{10} = \frac{50761933}{25}$$
Divide both parts of the equation by (-50761933*x/10 + 4320000*x*(1 + 5*x/2)/(2 + 5*x))/x
x = 50761933/25 / ((-50761933*x/10 + 4320000*x*(1 + 5*x/2)/(2 + 5*x))/x)
We get the answer: x = -101523866/145809665
Sum and product of roots
[src]
sum
-101523866 ----------- 145809665
$$- \frac{101523866}{145809665}$$
=
-101523866 ----------- 145809665
$$- \frac{101523866}{145809665}$$
product
-101523866 ----------- 145809665
$$- \frac{101523866}{145809665}$$
=
-101523866 ----------- 145809665
$$- \frac{101523866}{145809665}$$
-101523866/145809665
Rapid solution
[src]
-101523866
x1 = -----------
145809665
$$x_{1} = - \frac{101523866}{145809665}$$
x1 = -101523866/145809665