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- x^ two + five hundred and thirty-three . thirty-three *x+ twenty-nine thousand, one hundred and sixty-six . seven = zero
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Similar expressions
- x^2+533.33*x-29166.7=0
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x^2+533.33*x+29166.7=0 equation
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The solution
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[src]
2 53333*x 291667
x + ------- + ------ = 0
100 10
$$\left(x^{2} + \frac{53333 x}{100}\right) + \frac{291667}{10} = 0$$
Detail solution
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
$$a = 1$$
$$b = \frac{53333}{100}$$
$$c = \frac{291667}{10}$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{53333}{200} + \frac{\sqrt{1677740889}}{200}$$
$$x_{2} = - \frac{53333}{200} - \frac{\sqrt{1677740889}}{200}$$
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
$$a = 1$$
$$b = \frac{53333}{100}$$
$$c = \frac{291667}{10}$$
, then
D = b^2 - 4 * a * c =
(53333/100)^2 - 4 * (1) * (291667/10) = 1677740889/10000
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{53333}{200} + \frac{\sqrt{1677740889}}{200}$$
$$x_{2} = - \frac{53333}{200} - \frac{\sqrt{1677740889}}{200}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{53333}{100}$$
$$q = \frac{c}{a}$$
$$q = \frac{291667}{10}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{53333}{100}$$
$$x_{1} x_{2} = \frac{291667}{10}$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{53333}{100}$$
$$q = \frac{c}{a}$$
$$q = \frac{291667}{10}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{53333}{100}$$
$$x_{1} x_{2} = \frac{291667}{10}$$
Sum and product of roots
[src]
sum
____________ ____________ 53333 \/ 1677740889 53333 \/ 1677740889 - ----- - -------------- + - ----- + -------------- 200 200 200 200
$$\left(- \frac{53333}{200} - \frac{\sqrt{1677740889}}{200}\right) + \left(- \frac{53333}{200} + \frac{\sqrt{1677740889}}{200}\right)$$
=
-53333 ------- 100
$$- \frac{53333}{100}$$
product
/ ____________\ / ____________\ | 53333 \/ 1677740889 | | 53333 \/ 1677740889 | |- ----- - --------------|*|- ----- + --------------| \ 200 200 / \ 200 200 /
$$\left(- \frac{53333}{200} - \frac{\sqrt{1677740889}}{200}\right) \left(- \frac{53333}{200} + \frac{\sqrt{1677740889}}{200}\right)$$
=
291667 ------ 10
$$\frac{291667}{10}$$
291667/10
Rapid solution
[src]
____________
53333 \/ 1677740889
x1 = - ----- - --------------
200 200
$$x_{1} = - \frac{53333}{200} - \frac{\sqrt{1677740889}}{200}$$
____________
53333 \/ 1677740889
x2 = - ----- + --------------
200 200
$$x_{2} = - \frac{53333}{200} + \frac{\sqrt{1677740889}}{200}$$
x2 = -53333/200 + sqrt(1677740889)/200