Mister Exam
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Identical expressions
- seven hundred and fourteen ÷x- seven hundred and fourteen (x- twenty-five)= two
- 714÷x minus 714(x minus 25) equally 2
- seven hundred and fourteen ÷x minus seven hundred and fourteen (x minus twenty minus five) equally two
- 714÷x-714x-25=2
-
Similar expressions
- 714÷x+714(x-25)=2
- 714÷x-714(x+25)=2
714÷x-714(x-25)=2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
714 --- - 714*(x - 25) = 2 x
$$- 714 \left(x - 25\right) + \frac{714}{x} = 2$$
Detail solution
Given the equation:
$$- 714 \left(x - 25\right) + \frac{714}{x} = 2$$
Multiply the equation sides by the denominators:
and x
we get:
$$x \left(- 714 \left(x - 25\right) + \frac{714}{x}\right) = 2 x$$
$$- 714 x^{2} + 17850 x + 714 = 2 x$$
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$- 714 x^{2} + 17850 x + 714 = 2 x$$
to
$$- 714 x^{2} + 17848 x + 714 = 0$$
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
$$a = -714$$
$$b = 17848$$
$$c = 714$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{4462}{357} - \frac{\sqrt{20036893}}{357}$$
$$x_{2} = \frac{4462}{357} + \frac{\sqrt{20036893}}{357}$$
$$- 714 \left(x - 25\right) + \frac{714}{x} = 2$$
Multiply the equation sides by the denominators:
and x
we get:
$$x \left(- 714 \left(x - 25\right) + \frac{714}{x}\right) = 2 x$$
$$- 714 x^{2} + 17850 x + 714 = 2 x$$
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$- 714 x^{2} + 17850 x + 714 = 2 x$$
to
$$- 714 x^{2} + 17848 x + 714 = 0$$
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
$$a = -714$$
$$b = 17848$$
$$c = 714$$
, then
D = b^2 - 4 * a * c =
(17848)^2 - 4 * (-714) * (714) = 320590288
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{4462}{357} - \frac{\sqrt{20036893}}{357}$$
$$x_{2} = \frac{4462}{357} + \frac{\sqrt{20036893}}{357}$$
Rapid solution
[src]
__________
4462 \/ 20036893
x1 = ---- - ------------
357 357
$$x_{1} = \frac{4462}{357} - \frac{\sqrt{20036893}}{357}$$
__________
4462 \/ 20036893
x2 = ---- + ------------
357 357
$$x_{2} = \frac{4462}{357} + \frac{\sqrt{20036893}}{357}$$
x2 = 4462/357 + sqrt(20036893)/357
Sum and product of roots
[src]
sum
__________ __________ 4462 \/ 20036893 4462 \/ 20036893 ---- - ------------ + ---- + ------------ 357 357 357 357
$$\left(\frac{4462}{357} - \frac{\sqrt{20036893}}{357}\right) + \left(\frac{4462}{357} + \frac{\sqrt{20036893}}{357}\right)$$
=
8924 ---- 357
$$\frac{8924}{357}$$
product
/ __________\ / __________\ |4462 \/ 20036893 | |4462 \/ 20036893 | |---- - ------------|*|---- + ------------| \357 357 / \357 357 /
$$\left(\frac{4462}{357} - \frac{\sqrt{20036893}}{357}\right) \left(\frac{4462}{357} + \frac{\sqrt{20036893}}{357}\right)$$
=
-1
$$-1$$
-1