x^2+35x+70=0

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Solution for x^2+35x+70=0 equation: 


Simplifying
x2 + 35x + 70 = 0

Reorder the terms:
70 + 35x + x2 = 0

Solving
70 + 35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-70' to each side of the equation.
70 + 35x + -70 + x2 = 0 + -70

Reorder the terms:
70 + -70 + 35x + x2 = 0 + -70

Combine like terms: 70 + -70 = 0
0 + 35x + x2 = 0 + -70
35x + x2 = 0 + -70

Combine like terms: 0 + -70 = -70
35x + x2 = -70

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = -70 + 306.25

Reorder the terms:
306.25 + 35x + x2 = -70 + 306.25

Combine like terms: -70 + 306.25 = 236.25
306.25 + 35x + x2 = 236.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 236.25

Calculate the square root of the right side: 15.370426149

Break this problem into two subproblems by setting 
(x + 17.5) equal to 15.370426149 and -15.370426149.


Subproblem 1
x + 17.5 = 15.370426149

Simplifying
x + 17.5 = 15.370426149

Reorder the terms:
17.5 + x = 15.370426149

Solving
17.5 + x = 15.370426149

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = 15.370426149 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 15.370426149 + -17.5
x = 15.370426149 + -17.5

Combine like terms: 15.370426149 + -17.5 = -2.129573851
x = -2.129573851

Simplifying
x = -2.129573851


Subproblem 2
x + 17.5 = -15.370426149

Simplifying
x + 17.5 = -15.370426149

Reorder the terms:
17.5 + x = -15.370426149

Solving
17.5 + x = -15.370426149

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = -15.370426149 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -15.370426149 + -17.5
x = -15.370426149 + -17.5

Combine like terms: -15.370426149 + -17.5 = -32.870426149
x = -32.870426149

Simplifying
x = -32.870426149


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.129573851, -32.870426149}

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