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sqrt(3*x+1)=x-1 equation

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Numerical solution:

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The solution

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\/ 3*x + 1  = x - 1
3x+1=x−1\sqrt{3 x + 1} = x - 1
Simplify
Detail solution
Given the equation
3x+1=x−1\sqrt{3 x + 1} = x - 1
3x+1=x−1\sqrt{3 x + 1} = x - 1
We raise the equation sides to 2-th degree
3x+1=(x−1)23 x + 1 = \left(x - 1\right)^{2}
3x+1=x2−2x+13 x + 1 = x^{2} - 2 x + 1
Transfer the right side of the equation left part with negative sign
−x2+5x=0- x^{2} + 5 x = 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=5b = 5
c=0c = 0
, then
D = b^2 - 4 * a * c = 

(5)^2 - 4 * (-1) * (0) = 25

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

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

or
x1=0x_{1} = 0
x2=5x_{2} = 5

Because
3x+1=x−1\sqrt{3 x + 1} = x - 1
and
3x+1≥0\sqrt{3 x + 1} \geq 0
then
x−1≥0x - 1 \geq 0
or
1≤x1 \leq x
x<∞x < \infty
The final answer:
x2=5x_{2} = 5
The graph
02468-4-2101214-2020
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
5
55 
=
5
55 
product
5
55 
=
5
55 
5
Rapid solution [src] 
x1 = 5
x1=5x_{1} = 5 
x1 = 5
Numerical answer [src] 
x1 = 5.0
x1 = 5.0
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