16x^2+4x=70

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Solution for 16x^2+4x=70 equation: 


Simplifying
16x2 + 4x = 70

Reorder the terms:
4x + 16x2 = 70

Solving
4x + 16x2 = 70

Solving for variable 'x'.

Reorder the terms:
-70 + 4x + 16x2 = 70 + -70

Combine like terms: 70 + -70 = 0
-70 + 4x + 16x2 = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-35 + 2x + 8x2)' equal to zero and attempt to solve:

Simplifying
-35 + 2x + 8x2 = 0

Solving
-35 + 2x + 8x2 = 0

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

Divide each side by '8'.
-4.375 + 0.25x + x2 = 0

Move the constant term to the right:

Add '4.375' to each side of the equation.
-4.375 + 0.25x + 4.375 + x2 = 0 + 4.375

Reorder the terms:
-4.375 + 4.375 + 0.25x + x2 = 0 + 4.375

Combine like terms: -4.375 + 4.375 = 0.000
0.000 + 0.25x + x2 = 0 + 4.375
0.25x + x2 = 0 + 4.375

Combine like terms: 0 + 4.375 = 4.375
0.25x + x2 = 4.375

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = 4.375 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 4.375 + 0.015625

Combine like terms: 4.375 + 0.015625 = 4.390625
0.015625 + 0.25x + x2 = 4.390625

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 4.390625

Calculate the square root of the right side: 2.095381827

Break this problem into two subproblems by setting 
(x + 0.125) equal to 2.095381827 and -2.095381827.


Subproblem 1
x + 0.125 = 2.095381827

Simplifying
x + 0.125 = 2.095381827

Reorder the terms:
0.125 + x = 2.095381827

Solving
0.125 + x = 2.095381827

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = 2.095381827 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 2.095381827 + -0.125
x = 2.095381827 + -0.125

Combine like terms: 2.095381827 + -0.125 = 1.970381827
x = 1.970381827

Simplifying
x = 1.970381827


Subproblem 2
x + 0.125 = -2.095381827

Simplifying
x + 0.125 = -2.095381827

Reorder the terms:
0.125 + x = -2.095381827

Solving
0.125 + x = -2.095381827

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = -2.095381827 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -2.095381827 + -0.125
x = -2.095381827 + -0.125

Combine like terms: -2.095381827 + -0.125 = -2.220381827
x = -2.220381827

Simplifying
x = -2.220381827


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.970381827, -2.220381827}
Solution
x = {1.970381827, -2.220381827}

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