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

Solution for x(x+2)=5x^2+1 equation:

Simplifying
x(x + 2) = 5x2 + 1

Reorder the terms:
x(2 + x) = 5x2 + 1
(2 * x + x * x) = 5x2 + 1
(2x + x2) = 5x2 + 1

Reorder the terms:
2x + x2 = 1 + 5x2

Solving
2x + x2 = 1 + 5x2

Solving for variable 'x'.

Reorder the terms:
-1 + 2x + x2 + -5x2 = 1 + 5x2 + -1 + -5x2

Combine like terms: x2 + -5x2 = -4x2
-1 + 2x + -4x2 = 1 + 5x2 + -1 + -5x2

Reorder the terms:
-1 + 2x + -4x2 = 1 + -1 + 5x2 + -5x2

Combine like terms: 1 + -1 = 0
-1 + 2x + -4x2 = 0 + 5x2 + -5x2
-1 + 2x + -4x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-1 + 2x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.25 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -0.5x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -0.5x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -0.5x + x2 = 0 + -0.25
-0.5x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-0.5x + x2 = -0.25

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -0.25 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -0.25 + 0.0625

Combine like terms: -0.25 + 0.0625 = -0.1875
0.0625 + -0.5x + x2 = -0.1875

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -0.1875

Can't calculate square root of the right side.

The solution to this equation could not be determined.