x^2+3.5x-350=0

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Solution for x^2+3.5x-350=0 equation: 


Simplifying
x2 + 3.5x + -350 = 0

Reorder the terms:
-350 + 3.5x + x2 = 0

Solving
-350 + 3.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '350' to each side of the equation.
-350 + 3.5x + 350 + x2 = 0 + 350

Reorder the terms:
-350 + 350 + 3.5x + x2 = 0 + 350

Combine like terms: -350 + 350 = 0
0 + 3.5x + x2 = 0 + 350
3.5x + x2 = 0 + 350

Combine like terms: 0 + 350 = 350
3.5x + x2 = 350

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 350 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 350 + 3.0625

Combine like terms: 350 + 3.0625 = 353.0625
3.0625 + 3.5x + x2 = 353.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 353.0625

Calculate the square root of the right side: 18.789957424

Break this problem into two subproblems by setting 
(x + 1.75) equal to 18.789957424 and -18.789957424.


Subproblem 1
x + 1.75 = 18.789957424

Simplifying
x + 1.75 = 18.789957424

Reorder the terms:
1.75 + x = 18.789957424

Solving
1.75 + x = 18.789957424

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 18.789957424 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 18.789957424 + -1.75
x = 18.789957424 + -1.75

Combine like terms: 18.789957424 + -1.75 = 17.039957424
x = 17.039957424

Simplifying
x = 17.039957424


Subproblem 2
x + 1.75 = -18.789957424

Simplifying
x + 1.75 = -18.789957424

Reorder the terms:
1.75 + x = -18.789957424

Solving
1.75 + x = -18.789957424

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -18.789957424 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -18.789957424 + -1.75
x = -18.789957424 + -1.75

Combine like terms: -18.789957424 + -1.75 = -20.539957424
x = -20.539957424

Simplifying
x = -20.539957424


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.039957424, -20.539957424}

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