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Identical expressions
- (twenty thousand -2x)- zero ,01x(twenty thousand -2x)= fifteen thousand, eight hundred and forty-two
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Similar expressions
- (20000+2x)-0,01x(20000-2x)=15842
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(20000-2x)-0,01x(20000-2x)=15842 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
x
20000 - 2*x - ---*(20000 - 2*x) = 15842
100
$$- \frac{x}{100} \left(20000 - 2 x\right) + \left(20000 - 2 x\right) = 15842$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$- \frac{x}{100} \left(20000 - 2 x\right) + \left(20000 - 2 x\right) = 15842$$
to
$$\left(- \frac{x}{100} \left(20000 - 2 x\right) + \left(20000 - 2 x\right)\right) - 15842 = 0$$
Expand the expression in the equation
$$\left(- \frac{x}{100} \left(20000 - 2 x\right) + \left(20000 - 2 x\right)\right) - 15842 = 0$$
We get the quadratic equation
$$\frac{x^{2}}{50} - 202 x + 4158 = 0$$
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
$$a = \frac{1}{50}$$
$$b = -202$$
$$c = 4158$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 10 \sqrt{252946} + 5050$$
$$x_{2} = 5050 - 10 \sqrt{252946}$$
left part with negative sign.
The equation is transformed from
$$- \frac{x}{100} \left(20000 - 2 x\right) + \left(20000 - 2 x\right) = 15842$$
to
$$\left(- \frac{x}{100} \left(20000 - 2 x\right) + \left(20000 - 2 x\right)\right) - 15842 = 0$$
Expand the expression in the equation
$$\left(- \frac{x}{100} \left(20000 - 2 x\right) + \left(20000 - 2 x\right)\right) - 15842 = 0$$
We get the quadratic equation
$$\frac{x^{2}}{50} - 202 x + 4158 = 0$$
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
$$a = \frac{1}{50}$$
$$b = -202$$
$$c = 4158$$
, then
D = b^2 - 4 * a * c =
(-202)^2 - 4 * (1/50) * (4158) = 1011784/25
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 10 \sqrt{252946} + 5050$$
$$x_{2} = 5050 - 10 \sqrt{252946}$$
Rapid solution
[src]
________ x1 = 5050 - 10*\/ 252946
$$x_{1} = 5050 - 10 \sqrt{252946}$$
________ x2 = 5050 + 10*\/ 252946
$$x_{2} = 10 \sqrt{252946} + 5050$$
x2 = 10*sqrt(252946) + 5050
Sum and product of roots
[src]
sum
________ ________ 5050 - 10*\/ 252946 + 5050 + 10*\/ 252946
$$\left(5050 - 10 \sqrt{252946}\right) + \left(10 \sqrt{252946} + 5050\right)$$
=
10100
$$10100$$
product
/ ________\ / ________\ \5050 - 10*\/ 252946 /*\5050 + 10*\/ 252946 /
$$\left(5050 - 10 \sqrt{252946}\right) \left(10 \sqrt{252946} + 5050\right)$$
=
207900
$$207900$$
207900