2(x^2+4x-35)=0

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Solution for 2(x^2+4x-35)=0 equation: 


Simplifying
2(x2 + 4x + -35) = 0

Reorder the terms:
2(-35 + 4x + x2) = 0
(-35 * 2 + 4x * 2 + x2 * 2) = 0
(-70 + 8x + 2x2) = 0

Solving
-70 + 8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-35 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-35 + 4x + x2 = 0

Solving
-35 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 4x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + 4x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 4x + x2 = 0 + 35
4x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
4x + x2 = 35

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 35 + 4

Reorder the terms:
4 + 4x + x2 = 35 + 4

Combine like terms: 35 + 4 = 39
4 + 4x + x2 = 39

Factor a perfect square on the left side:
(x + 2)(x + 2) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(x + 2) equal to 6.244997998 and -6.244997998.


Subproblem 1
x + 2 = 6.244997998

Simplifying
x + 2 = 6.244997998

Reorder the terms:
2 + x = 6.244997998

Solving
2 + x = 6.244997998

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 6.244997998 + -2

Combine like terms: 2 + -2 = 0
0 + x = 6.244997998 + -2
x = 6.244997998 + -2

Combine like terms: 6.244997998 + -2 = 4.244997998
x = 4.244997998

Simplifying
x = 4.244997998


Subproblem 2
x + 2 = -6.244997998

Simplifying
x + 2 = -6.244997998

Reorder the terms:
2 + x = -6.244997998

Solving
2 + x = -6.244997998

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -6.244997998 + -2

Combine like terms: 2 + -2 = 0
0 + x = -6.244997998 + -2
x = -6.244997998 + -2

Combine like terms: -6.244997998 + -2 = -8.244997998
x = -8.244997998

Simplifying
x = -8.244997998


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.244997998, -8.244997998}
Solution
x = {4.244997998, -8.244997998}

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