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sqrt(3+2*x)=x

sqrt(3+2*x)=x equation

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Numerical solution:

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The solution

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\/ 3 + 2*x  = x
2x+3=x\sqrt{2 x + 3} = x
Simplify
Detail solution
Given the equation
2x+3=x\sqrt{2 x + 3} = x
2x+3=x\sqrt{2 x + 3} = x
We raise the equation sides to 2-th degree
2x+3=x22 x + 3 = x^{2}
2x+3=x22 x + 3 = x^{2}
Transfer the right side of the equation left part with negative sign
−x2+2x+3=0- x^{2} + 2 x + 3 = 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=2b = 2
c=3c = 3
, then
D = b^2 - 4 * a * c = 

(2)^2 - 4 * (-1) * (3) = 16

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=3x_{2} = 3

Because
2x+3=x\sqrt{2 x + 3} = x
and
2x+3≥0\sqrt{2 x + 3} \geq 0
then
x≥0x \geq 0
or
0≤x0 \leq x
x<∞x < \infty
The final answer:
x2=3x_{2} = 3
The graph
02468-6-4-21012-2020
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
3
33 
=
3
33 
product
3
33 
=
3
33 
3
Rapid solution [src] 
x1 = 3
x1=3x_{1} = 3 
x1 = 3
Numerical answer [src] 
x1 = 3.0
x1 = 3.0
The graph
sqrt(3+2*x)=x equation
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