4x^2+4x-70=0

Solution for 4x^2+4x-70=0 equation:

Simplifying
4x2 + 4x + -70 = 0

Reorder the terms:
-70 + 4x + 4x2 = 0

Solving
-70 + 4x + 4x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-35 + 2x + 2x2)' equal to zero and attempt to solve:

Simplifying
-35 + 2x + 2x2 = 0

Solving
-35 + 2x + 2x2 = 0

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

Divide each side by '2'.
-17.5 + x + x2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + x + 17.5 + x2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + x + x2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x + x2 = 0 + 17.5
x + x2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
x + x2 = 17.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 17.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 17.5 + 0.25

Combine like terms: 17.5 + 0.25 = 17.75
1.25 + x2 = 17.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 17.75

Calculate the square root of the right side: 4.213074887

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.213074887 and -4.213074887.

Subproblem 1
x + 0.5 = 4.213074887

Simplifying
x + 0.5 = 4.213074887

Reorder the terms:
0.5 + x = 4.213074887

Solving
0.5 + x = 4.213074887

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 4.213074887 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.213074887 + -0.5
x = 4.213074887 + -0.5

Combine like terms: 4.213074887 + -0.5 = 3.713074887
x = 3.713074887

Simplifying
x = 3.713074887

Subproblem 2
x + 0.5 = -4.213074887

Simplifying
x + 0.5 = -4.213074887

Reorder the terms:
0.5 + x = -4.213074887

Solving
0.5 + x = -4.213074887

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -4.213074887 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.213074887 + -0.5
x = -4.213074887 + -0.5

Combine like terms: -4.213074887 + -0.5 = -4.713074887
x = -4.713074887

Simplifying
x = -4.713074887

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.713074887, -4.713074887}
Solution
x = {3.713074887, -4.713074887}