x^2+2x+3x=700

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Solution for x^2+2x+3x=700 equation: 


Simplifying
x2 + 2x + 3x = 700

Reorder the terms:
2x + 3x + x2 = 700

Combine like terms: 2x + 3x = 5x
5x + x2 = 700

Solving
5x + x2 = 700

Solving for variable 'x'.

Reorder the terms:
-700 + 5x + x2 = 700 + -700

Combine like terms: 700 + -700 = 0
-700 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '700' to each side of the equation.
-700 + 5x + 700 + x2 = 0 + 700

Reorder the terms:
-700 + 700 + 5x + x2 = 0 + 700

Combine like terms: -700 + 700 = 0
0 + 5x + x2 = 0 + 700
5x + x2 = 0 + 700

Combine like terms: 0 + 700 = 700
5x + x2 = 700

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 700 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 700 + 6.25

Combine like terms: 700 + 6.25 = 706.25
6.25 + 5x + x2 = 706.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 706.25

Calculate the square root of the right side: 26.575364532

Break this problem into two subproblems by setting 
(x + 2.5) equal to 26.575364532 and -26.575364532.


Subproblem 1
x + 2.5 = 26.575364532

Simplifying
x + 2.5 = 26.575364532

Reorder the terms:
2.5 + x = 26.575364532

Solving
2.5 + x = 26.575364532

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 26.575364532 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 26.575364532 + -2.5
x = 26.575364532 + -2.5

Combine like terms: 26.575364532 + -2.5 = 24.075364532
x = 24.075364532

Simplifying
x = 24.075364532


Subproblem 2
x + 2.5 = -26.575364532

Simplifying
x + 2.5 = -26.575364532

Reorder the terms:
2.5 + x = -26.575364532

Solving
2.5 + x = -26.575364532

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -26.575364532 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -26.575364532 + -2.5
x = -26.575364532 + -2.5

Combine like terms: -26.575364532 + -2.5 = -29.075364532
x = -29.075364532

Simplifying
x = -29.075364532


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.075364532, -29.075364532}

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