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x^2+30=-11x

x^2+30=-11x equation

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Numerical solution:

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The solution

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 2             
x  + 30 = -11*x
x2+30=−11xx^{2} + 30 = - 11 x
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
x2+30=−11xx^{2} + 30 = - 11 x
to
11x+(x2+30)=011 x + \left(x^{2} + 30\right) = 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:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=11b = 11
c=30c = 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
x1=−5x_{1} = -5
x2=−6x_{2} = -6
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=11p = 11
q=caq = \frac{c}{a}
q=30q = 30
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−11x_{1} + x_{2} = -11
x1x2=30x_{1} x_{2} = 30
The graph
024-16-14-12-10-8-6-4-2-500500
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -6
x1=−6x_{1} = -6 
x2 = -5
x2=−5x_{2} = -5 
x2 = -5
Sum and product of roots [src] 
sum
-6 - 5
−6−5-6 - 5 
=
-11
−11-11 
product
-6*(-5)
−−30- -30 
=
30
3030 
30
Numerical answer [src] 
x1 = -6.0
x2 = -5.0
x2 = -5.0
The graph
x^2+30=-11x equation
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