x^2+3x+4.5=4

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Solution for x^2+3x+4.5=4 equation: 


Simplifying
x2 + 3x + 4.5 = 4

Reorder the terms:
4.5 + 3x + x2 = 4

Solving
4.5 + 3x + x2 = 4

Solving for variable 'x'.

Reorder the terms:
4.5 + -4 + 3x + x2 = 4 + -4

Combine like terms: 4.5 + -4 = 0.5
0.5 + 3x + x2 = 4 + -4

Combine like terms: 4 + -4 = 0
0.5 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 3x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 3x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 3x + x2 = 0 + -0.5
3x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
3x + x2 = -0.5

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -0.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -0.5 + 2.25

Combine like terms: -0.5 + 2.25 = 1.75
2.25 + 3x + x2 = 1.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.322875656 and -1.322875656.


Subproblem 1
x + 1.5 = 1.322875656

Simplifying
x + 1.5 = 1.322875656

Reorder the terms:
1.5 + x = 1.322875656

Solving
1.5 + x = 1.322875656

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 1.322875656 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.322875656 + -1.5
x = 1.322875656 + -1.5

Combine like terms: 1.322875656 + -1.5 = -0.177124344
x = -0.177124344

Simplifying
x = -0.177124344


Subproblem 2
x + 1.5 = -1.322875656

Simplifying
x + 1.5 = -1.322875656

Reorder the terms:
1.5 + x = -1.322875656

Solving
1.5 + x = -1.322875656

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -1.322875656 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.322875656 + -1.5
x = -1.322875656 + -1.5

Combine like terms: -1.322875656 + -1.5 = -2.822875656
x = -2.822875656

Simplifying
x = -2.822875656


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.177124344, -2.822875656}

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