x^2+7x+2.25=0

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Solution for x^2+7x+2.25=0 equation: 


Simplifying
x2 + 7x + 2.25 = 0

Reorder the terms:
2.25 + 7x + x2 = 0

Solving
2.25 + 7x + 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 + 7x + -2.25 + x2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + 7x + x2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + 7x + x2 = 0 + -2.25
7x + x2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
7x + x2 = -2.25

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -2.25 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -2.25 + 12.25

Combine like terms: -2.25 + 12.25 = 10
12.25 + 7x + x2 = 10

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.16227766 and -3.16227766.


Subproblem 1
x + 3.5 = 3.16227766

Simplifying
x + 3.5 = 3.16227766

Reorder the terms:
3.5 + x = 3.16227766

Solving
3.5 + x = 3.16227766

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 3.16227766 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 3.16227766 + -3.5
x = 3.16227766 + -3.5

Combine like terms: 3.16227766 + -3.5 = -0.33772234
x = -0.33772234

Simplifying
x = -0.33772234


Subproblem 2
x + 3.5 = -3.16227766

Simplifying
x + 3.5 = -3.16227766

Reorder the terms:
3.5 + x = -3.16227766

Solving
3.5 + x = -3.16227766

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -3.16227766 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -3.16227766 + -3.5
x = -3.16227766 + -3.5

Combine like terms: -3.16227766 + -3.5 = -6.66227766
x = -6.66227766

Simplifying
x = -6.66227766


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.33772234, -6.66227766}

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