x^2+4x-2.25=0

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Solution for x^2+4x-2.25=0 equation: 


Simplifying
x2 + 4x + -2.25 = 0

Reorder the terms:
-2.25 + 4x + x2 = 0

Solving
-2.25 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 4x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 4x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 4x + x2 = 0 + 2.25
4x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
4x + x2 = 2.25

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 2.25 + 4

Reorder the terms:
4 + 4x + x2 = 2.25 + 4

Combine like terms: 2.25 + 4 = 6.25
4 + 4x + x2 = 6.25

Factor a perfect square on the left side:
(x + 2)(x + 2) = 6.25

Calculate the square root of the right side: 2.5

Break this problem into two subproblems by setting 
(x + 2) equal to 2.5 and -2.5.


Subproblem 1
x + 2 = 2.5

Simplifying
x + 2 = 2.5

Reorder the terms:
2 + x = 2.5

Solving
2 + x = 2.5

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 2.5 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.5 + -2
x = 2.5 + -2

Combine like terms: 2.5 + -2 = 0.5
x = 0.5

Simplifying
x = 0.5


Subproblem 2
x + 2 = -2.5

Simplifying
x + 2 = -2.5

Reorder the terms:
2 + x = -2.5

Solving
2 + x = -2.5

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = -2.5 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.5 + -2
x = -2.5 + -2

Combine like terms: -2.5 + -2 = -4.5
x = -4.5

Simplifying
x = -4.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -4.5}

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