(x+2)(x+2)+x(x-3)=1

Solution for (x+2)(x+2)+x(x-3)=1 equation:

Simplifying
(x + 2)(x + 2) + x(x + -3) = 1

Reorder the terms:
(2 + x)(x + 2) + x(x + -3) = 1

Reorder the terms:
(2 + x)(2 + x) + x(x + -3) = 1

Multiply (2 + x) * (2 + x)
(2(2 + x) + x(2 + x)) + x(x + -3) = 1
((2 * 2 + x * 2) + x(2 + x)) + x(x + -3) = 1
((4 + 2x) + x(2 + x)) + x(x + -3) = 1
(4 + 2x + (2 * x + x * x)) + x(x + -3) = 1
(4 + 2x + (2x + x2)) + x(x + -3) = 1

Combine like terms: 2x + 2x = 4x
(4 + 4x + x2) + x(x + -3) = 1

Reorder the terms:
4 + 4x + x2 + x(-3 + x) = 1
4 + 4x + x2 + (-3 * x + x * x) = 1
4 + 4x + x2 + (-3x + x2) = 1

Reorder the terms:
4 + 4x + -3x + x2 + x2 = 1

Combine like terms: 4x + -3x = 1x
4 + 1x + x2 + x2 = 1

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

Solving
4 + 1x + 2x2 = 1

Solving for variable 'x'.

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

Combine like terms: 4 + -1 = 3
3 + 1x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
3 + 1x + 2x2 = 0

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

Divide each side by '2'.
1.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 0.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 0.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.5x + x2 = 0 + -1.5
0.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
0.5x + x2 = -1.5

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 = -1.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = -1.5 + 0.0625

Combine like terms: -1.5 + 0.0625 = -1.4375
0.0625 + 0.5x + x2 = -1.4375

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = -1.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.