x^2+3x=1400

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Solution for x^2+3x=1400 equation: 


Simplifying
x2 + 3x = 1400

Reorder the terms:
3x + x2 = 1400

Solving
3x + x2 = 1400

Solving for variable 'x'.

Reorder the terms:
-1400 + 3x + x2 = 1400 + -1400

Combine like terms: 1400 + -1400 = 0
-1400 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1400' to each side of the equation.
-1400 + 3x + 1400 + x2 = 0 + 1400

Reorder the terms:
-1400 + 1400 + 3x + x2 = 0 + 1400

Combine like terms: -1400 + 1400 = 0
0 + 3x + x2 = 0 + 1400
3x + x2 = 0 + 1400

Combine like terms: 0 + 1400 = 1400
3x + x2 = 1400

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 = 1400 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 1400 + 2.25

Combine like terms: 1400 + 2.25 = 1402.25
2.25 + 3x + x2 = 1402.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 1402.25

Calculate the square root of the right side: 37.446628687

Break this problem into two subproblems by setting 
(x + 1.5) equal to 37.446628687 and -37.446628687.


Subproblem 1
x + 1.5 = 37.446628687

Simplifying
x + 1.5 = 37.446628687

Reorder the terms:
1.5 + x = 37.446628687

Solving
1.5 + x = 37.446628687

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 = 37.446628687 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 37.446628687 + -1.5
x = 37.446628687 + -1.5

Combine like terms: 37.446628687 + -1.5 = 35.946628687
x = 35.946628687

Simplifying
x = 35.946628687


Subproblem 2
x + 1.5 = -37.446628687

Simplifying
x + 1.5 = -37.446628687

Reorder the terms:
1.5 + x = -37.446628687

Solving
1.5 + x = -37.446628687

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 = -37.446628687 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -37.446628687 + -1.5
x = -37.446628687 + -1.5

Combine like terms: -37.446628687 + -1.5 = -38.946628687
x = -38.946628687

Simplifying
x = -38.946628687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.946628687, -38.946628687}

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