3x^2+5x-35=0

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Solution for 3x^2+5x-35=0 equation: 


Simplifying
3x2 + 5x + -35 = 0

Reorder the terms:
-35 + 5x + 3x2 = 0

Solving
-35 + 5x + 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 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '11.66666667' to each side of the equation.
-11.66666667 + 1.666666667x + 11.66666667 + x2 = 0 + 11.66666667

Reorder the terms:
-11.66666667 + 11.66666667 + 1.666666667x + x2 = 0 + 11.66666667

Combine like terms: -11.66666667 + 11.66666667 = 0.00000000
0.00000000 + 1.666666667x + x2 = 0 + 11.66666667
1.666666667x + x2 = 0 + 11.66666667

Combine like terms: 0 + 11.66666667 = 11.66666667
1.666666667x + x2 = 11.66666667

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 11.66666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 11.66666667 + 0.6944444447

Combine like terms: 11.66666667 + 0.6944444447 = 12.3611111147
0.6944444447 + 1.666666667x + x2 = 12.3611111147

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 12.3611111147

Calculate the square root of the right side: 3.515837185

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 3.515837185 and -3.515837185.


Subproblem 1
x + 0.8333333335 = 3.515837185

Simplifying
x + 0.8333333335 = 3.515837185

Reorder the terms:
0.8333333335 + x = 3.515837185

Solving
0.8333333335 + x = 3.515837185

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 3.515837185 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 3.515837185 + -0.8333333335
x = 3.515837185 + -0.8333333335

Combine like terms: 3.515837185 + -0.8333333335 = 2.6825038515
x = 2.6825038515

Simplifying
x = 2.6825038515


Subproblem 2
x + 0.8333333335 = -3.515837185

Simplifying
x + 0.8333333335 = -3.515837185

Reorder the terms:
0.8333333335 + x = -3.515837185

Solving
0.8333333335 + x = -3.515837185

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -3.515837185 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -3.515837185 + -0.8333333335
x = -3.515837185 + -0.8333333335

Combine like terms: -3.515837185 + -0.8333333335 = -4.3491705185
x = -4.3491705185

Simplifying
x = -4.3491705185


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.6825038515, -4.3491705185}

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