x^2+3.01x+2.25=0

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Solution for x^2+3.01x+2.25=0 equation: 


Simplifying
x2 + 3.01x + 2.25 = 0

Reorder the terms:
2.25 + 3.01x + x2 = 0

Solving
2.25 + 3.01x + 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 + 3.01x + -2.25 + x2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + 3.01x + x2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + 3.01x + x2 = 0 + -2.25
3.01x + x2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
3.01x + x2 = -2.25

The x term is 3.01x.  Take half its coefficient (1.505).
Square it (2.265025) and add it to both sides.

Add '2.265025' to each side of the equation.
3.01x + 2.265025 + x2 = -2.25 + 2.265025

Reorder the terms:
2.265025 + 3.01x + x2 = -2.25 + 2.265025

Combine like terms: -2.25 + 2.265025 = 0.015025
2.265025 + 3.01x + x2 = 0.015025

Factor a perfect square on the left side:
(x + 1.505)(x + 1.505) = 0.015025

Calculate the square root of the right side: 0.122576507

Break this problem into two subproblems by setting 
(x + 1.505) equal to 0.122576507 and -0.122576507.


Subproblem 1
x + 1.505 = 0.122576507

Simplifying
x + 1.505 = 0.122576507

Reorder the terms:
1.505 + x = 0.122576507

Solving
1.505 + x = 0.122576507

Solving for variable 'x'.

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

Add '-1.505' to each side of the equation.
1.505 + -1.505 + x = 0.122576507 + -1.505

Combine like terms: 1.505 + -1.505 = 0.000
0.000 + x = 0.122576507 + -1.505
x = 0.122576507 + -1.505

Combine like terms: 0.122576507 + -1.505 = -1.382423493
x = -1.382423493

Simplifying
x = -1.382423493


Subproblem 2
x + 1.505 = -0.122576507

Simplifying
x + 1.505 = -0.122576507

Reorder the terms:
1.505 + x = -0.122576507

Solving
1.505 + x = -0.122576507

Solving for variable 'x'.

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

Add '-1.505' to each side of the equation.
1.505 + -1.505 + x = -0.122576507 + -1.505

Combine like terms: 1.505 + -1.505 = 0.000
0.000 + x = -0.122576507 + -1.505
x = -0.122576507 + -1.505

Combine like terms: -0.122576507 + -1.505 = -1.627576507
x = -1.627576507

Simplifying
x = -1.627576507


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.382423493, -1.627576507}

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