2x^2+16x-70=0

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Solution for 2x^2+16x-70=0 equation: 


Simplifying
2x2 + 16x + -70 = 0

Reorder the terms:
-70 + 16x + 2x2 = 0

Solving
-70 + 16x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + 8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-35 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-35 + 8x + x2 = 0

Solving
-35 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 8x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + 8x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 8x + x2 = 0 + 35
8x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
8x + x2 = 35

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 35 + 16

Reorder the terms:
16 + 8x + x2 = 35 + 16

Combine like terms: 35 + 16 = 51
16 + 8x + x2 = 51

Factor a perfect square on the left side:
(x + 4)(x + 4) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(x + 4) equal to 7.141428429 and -7.141428429.


Subproblem 1
x + 4 = 7.141428429

Simplifying
x + 4 = 7.141428429

Reorder the terms:
4 + x = 7.141428429

Solving
4 + x = 7.141428429

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 7.141428429 + -4

Combine like terms: 4 + -4 = 0
0 + x = 7.141428429 + -4
x = 7.141428429 + -4

Combine like terms: 7.141428429 + -4 = 3.141428429
x = 3.141428429

Simplifying
x = 3.141428429


Subproblem 2
x + 4 = -7.141428429

Simplifying
x + 4 = -7.141428429

Reorder the terms:
4 + x = -7.141428429

Solving
4 + x = -7.141428429

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -7.141428429 + -4

Combine like terms: 4 + -4 = 0
0 + x = -7.141428429 + -4
x = -7.141428429 + -4

Combine like terms: -7.141428429 + -4 = -11.141428429
x = -11.141428429

Simplifying
x = -11.141428429


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.141428429, -11.141428429}
Solution
x = {3.141428429, -11.141428429}

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