705x-21000+70x+x^2=0

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Solution for 705x-21000+70x+x^2=0 equation: 


Simplifying
705x + -21000 + 70x + x2 = 0

Reorder the terms:
-21000 + 705x + 70x + x2 = 0

Combine like terms: 705x + 70x = 775x
-21000 + 775x + x2 = 0

Solving
-21000 + 775x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '21000' to each side of the equation.
-21000 + 775x + 21000 + x2 = 0 + 21000

Reorder the terms:
-21000 + 21000 + 775x + x2 = 0 + 21000

Combine like terms: -21000 + 21000 = 0
0 + 775x + x2 = 0 + 21000
775x + x2 = 0 + 21000

Combine like terms: 0 + 21000 = 21000
775x + x2 = 21000

The x term is 775x.  Take half its coefficient (387.5).
Square it (150156.25) and add it to both sides.

Add '150156.25' to each side of the equation.
775x + 150156.25 + x2 = 21000 + 150156.25

Reorder the terms:
150156.25 + 775x + x2 = 21000 + 150156.25

Combine like terms: 21000 + 150156.25 = 171156.25
150156.25 + 775x + x2 = 171156.25

Factor a perfect square on the left side:
(x + 387.5)(x + 387.5) = 171156.25

Calculate the square root of the right side: 413.710345532

Break this problem into two subproblems by setting 
(x + 387.5) equal to 413.710345532 and -413.710345532.


Subproblem 1
x + 387.5 = 413.710345532

Simplifying
x + 387.5 = 413.710345532

Reorder the terms:
387.5 + x = 413.710345532

Solving
387.5 + x = 413.710345532

Solving for variable 'x'.

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

Add '-387.5' to each side of the equation.
387.5 + -387.5 + x = 413.710345532 + -387.5

Combine like terms: 387.5 + -387.5 = 0.0
0.0 + x = 413.710345532 + -387.5
x = 413.710345532 + -387.5

Combine like terms: 413.710345532 + -387.5 = 26.210345532
x = 26.210345532

Simplifying
x = 26.210345532


Subproblem 2
x + 387.5 = -413.710345532

Simplifying
x + 387.5 = -413.710345532

Reorder the terms:
387.5 + x = -413.710345532

Solving
387.5 + x = -413.710345532

Solving for variable 'x'.

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

Add '-387.5' to each side of the equation.
387.5 + -387.5 + x = -413.710345532 + -387.5

Combine like terms: 387.5 + -387.5 = 0.0
0.0 + x = -413.710345532 + -387.5
x = -413.710345532 + -387.5

Combine like terms: -413.710345532 + -387.5 = -801.210345532
x = -801.210345532

Simplifying
x = -801.210345532


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.210345532, -801.210345532}

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