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x^2-11*x+30=0

x^2-11*x+30=0 equation

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Numerical solution:

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The solution

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x  - 11*x + 30 = 0
$$\left(x^{2} - 11 x\right) + 30 = 0$$
Detail solution
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
$$a = 1$$
$$b = -11$$
$$c = 30$$
, then
D = b^2 - 4 * a * c = 

(-11)^2 - 4 * (1) * (30) = 1

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
$$x_{1} = 6$$
$$x_{2} = 5$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -11$$
$$q = \frac{c}{a}$$
$$q = 30$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 11$$
$$x_{1} x_{2} = 30$$
The graph
Rapid solution [src]
x1 = 5
$$x_{1} = 5$$
x2 = 6
$$x_{2} = 6$$
x2 = 6
Sum and product of roots [src]
sum
5 + 6
$$5 + 6$$
=
11
$$11$$
product
5*6
$$5 \cdot 6$$
=
30
$$30$$
30
Numerical answer [src]
x1 = 6.0
x2 = 5.0
x2 = 5.0
The graph
x^2-11*x+30=0 equation