What is the answer to sqrt(x^2+5x+1)=2x-1 ?

The answer to sqrt(x^2+5x+1)=2x-1 is x=3

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sqrt(x^2+5x+1)=2x-1

x^{2} + 5 x + 1 = 2 x - 1

x = 3

Solution steps

x^{2} + 5 x + 1 = 2 x - 1

Square both sides:

x^{2} + 5 x + 1 = 4 x^{2} - 4 x + 1

x^{2} + 5 x + 1 = 4 x^{2} - 4 x + 1

Solve

x^{2} + 5 x + 1 = 4 x^{2} - 4 x + 1 : x = 0, x = 3

x = 0, x = 3

Verify Solutions:

x = 0

False

, x = 3

True

The solution is

x = 3

\frac{4 x + 40}{17} = 4

2 x - 1 + x + 4 = 3 x - 1

x - 10 = x + 3

x + 1 + 3 = 2 x + 5

- 6 x + 30 = x - 5

What is the answer to sqrt(x^2+5x+1)=2x-1 ?
The answer to sqrt(x^2+5x+1)=2x-1 is x=3
Solve for x: sqrt(x^2+5x+1)=2x-1
The solution is x=3