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sqrt(10x+11)=-x equation

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Numerical solution:

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The solution

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  ___________     
\/ 10*x + 11  = -x
10x+11=−x\sqrt{10 x + 11} = - x
Simplify
Detail solution
Given the equation
10x+11=−x\sqrt{10 x + 11} = - x
10x+11=−x\sqrt{10 x + 11} = - x
We raise the equation sides to 2-th degree
10x+11=x210 x + 11 = x^{2}
10x+11=x210 x + 11 = x^{2}
Transfer the right side of the equation left part with negative sign
−x2+10x+11=0- x^{2} + 10 x + 11 = 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=10b = 10
c=11c = 11
, then
D = b^2 - 4 * a * c = 

(10)^2 - 4 * (-1) * (11) = 144

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

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

or
x1=−1x_{1} = -1
x2=11x_{2} = 11

Because
10x+11=−x\sqrt{10 x + 11} = - x
and
10x+11≥0\sqrt{10 x + 11} \geq 0
then
−x≥0- x \geq 0
or
x≤0x \leq 0
−∞<x-\infty < x
The final answer:
x1=−1x_{1} = -1
The graph
02468-10-8-6-4-2-2020
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-1
−1-1 
=
-1
−1-1 
product
-1
−1-1 
=
-1
−1-1 
-1
Rapid solution [src] 
x1 = -1
x1=−1x_{1} = -1 
x1 = -1
Numerical answer [src] 
x1 = -1.0
x1 = -1.0
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