3x^2+15x-35=0

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Solution for 3x^2+15x-35=0 equation: 


Simplifying
3x2 + 15x + -35 = 0

Reorder the terms:
-35 + 15x + 3x2 = 0

Solving
-35 + 15x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-11.66666667 + 5x + x2 = 0

Move the constant term to the right:

Add '11.66666667' to each side of the equation.
-11.66666667 + 5x + 11.66666667 + x2 = 0 + 11.66666667

Reorder the terms:
-11.66666667 + 11.66666667 + 5x + x2 = 0 + 11.66666667

Combine like terms: -11.66666667 + 11.66666667 = 0.00000000
0.00000000 + 5x + x2 = 0 + 11.66666667
5x + x2 = 0 + 11.66666667

Combine like terms: 0 + 11.66666667 = 11.66666667
5x + x2 = 11.66666667

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 = 11.66666667 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 11.66666667 + 6.25

Combine like terms: 11.66666667 + 6.25 = 17.91666667
6.25 + 5x + x2 = 17.91666667

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 17.91666667

Calculate the square root of the right side: 4.232808367

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.232808367 and -4.232808367.


Subproblem 1
x + 2.5 = 4.232808367

Simplifying
x + 2.5 = 4.232808367

Reorder the terms:
2.5 + x = 4.232808367

Solving
2.5 + x = 4.232808367

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 = 4.232808367 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 4.232808367 + -2.5
x = 4.232808367 + -2.5

Combine like terms: 4.232808367 + -2.5 = 1.732808367
x = 1.732808367

Simplifying
x = 1.732808367


Subproblem 2
x + 2.5 = -4.232808367

Simplifying
x + 2.5 = -4.232808367

Reorder the terms:
2.5 + x = -4.232808367

Solving
2.5 + x = -4.232808367

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 = -4.232808367 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -4.232808367 + -2.5
x = -4.232808367 + -2.5

Combine like terms: -4.232808367 + -2.5 = -6.732808367
x = -6.732808367

Simplifying
x = -6.732808367


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.732808367, -6.732808367}

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