x^2+4x+1.5=1350

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Solution for x^2+4x+1.5=1350 equation: 


Simplifying
x2 + 4x + 1.5 = 1350

Reorder the terms:
1.5 + 4x + x2 = 1350

Solving
1.5 + 4x + x2 = 1350

Solving for variable 'x'.

Reorder the terms:
1.5 + -1350 + 4x + x2 = 1350 + -1350

Combine like terms: 1.5 + -1350 = -1348.5
-1348.5 + 4x + x2 = 1350 + -1350

Combine like terms: 1350 + -1350 = 0
-1348.5 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1348.5' to each side of the equation.
-1348.5 + 4x + 1348.5 + x2 = 0 + 1348.5

Reorder the terms:
-1348.5 + 1348.5 + 4x + x2 = 0 + 1348.5

Combine like terms: -1348.5 + 1348.5 = 0.0
0.0 + 4x + x2 = 0 + 1348.5
4x + x2 = 0 + 1348.5

Combine like terms: 0 + 1348.5 = 1348.5
4x + x2 = 1348.5

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 = 1348.5 + 4

Reorder the terms:
4 + 4x + x2 = 1348.5 + 4

Combine like terms: 1348.5 + 4 = 1352.5
4 + 4x + x2 = 1352.5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 1352.5

Calculate the square root of the right side: 36.776351097

Break this problem into two subproblems by setting 
(x + 2) equal to 36.776351097 and -36.776351097.


Subproblem 1
x + 2 = 36.776351097

Simplifying
x + 2 = 36.776351097

Reorder the terms:
2 + x = 36.776351097

Solving
2 + x = 36.776351097

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 = 36.776351097 + -2

Combine like terms: 2 + -2 = 0
0 + x = 36.776351097 + -2
x = 36.776351097 + -2

Combine like terms: 36.776351097 + -2 = 34.776351097
x = 34.776351097

Simplifying
x = 34.776351097


Subproblem 2
x + 2 = -36.776351097

Simplifying
x + 2 = -36.776351097

Reorder the terms:
2 + x = -36.776351097

Solving
2 + x = -36.776351097

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 = -36.776351097 + -2

Combine like terms: 2 + -2 = 0
0 + x = -36.776351097 + -2
x = -36.776351097 + -2

Combine like terms: -36.776351097 + -2 = -38.776351097
x = -38.776351097

Simplifying
x = -38.776351097


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.776351097, -38.776351097}

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