7x^2+4x-16=0

Solution for 7x^2+4x-16=0 equation:

Simplifying
7x2 + 4x + -16 = 0

Reorder the terms:
-16 + 4x + 7x2 = 0

Solving
-16 + 4x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-2.285714286 + 0.5714285714x + x2 = 0

Move the constant term to the right:

Add '2.285714286' to each side of the equation.
-2.285714286 + 0.5714285714x + 2.285714286 + x2 = 0 + 2.285714286

Reorder the terms:
-2.285714286 + 2.285714286 + 0.5714285714x + x2 = 0 + 2.285714286

Combine like terms: -2.285714286 + 2.285714286 = 0.000000000
0.000000000 + 0.5714285714x + x2 = 0 + 2.285714286
0.5714285714x + x2 = 0 + 2.285714286

Combine like terms: 0 + 2.285714286 = 2.285714286
0.5714285714x + x2 = 2.285714286

The x term is 0.5714285714x.  Take half its coefficient (0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
0.5714285714x + 0.08163265305 + x2 = 2.285714286 + 0.08163265305

Reorder the terms:
0.08163265305 + 0.5714285714x + x2 = 2.285714286 + 0.08163265305

Combine like terms: 2.285714286 + 0.08163265305 = 2.36734693905
0.08163265305 + 0.5714285714x + x2 = 2.36734693905

Factor a perfect square on the left side:
(x + 0.2857142857)(x + 0.2857142857) = 2.36734693905

Calculate the square root of the right side: 1.538618516

Break this problem into two subproblems by setting 
(x + 0.2857142857) equal to 1.538618516 and -1.538618516.

Subproblem 1
x + 0.2857142857 = 1.538618516

Simplifying
x + 0.2857142857 = 1.538618516

Reorder the terms:
0.2857142857 + x = 1.538618516

Solving
0.2857142857 + x = 1.538618516

Solving for variable 'x'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + x = 1.538618516 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = 1.538618516 + -0.2857142857
x = 1.538618516 + -0.2857142857

Combine like terms: 1.538618516 + -0.2857142857 = 1.2529042303
x = 1.2529042303

Simplifying
x = 1.2529042303

Subproblem 2
x + 0.2857142857 = -1.538618516

Simplifying
x + 0.2857142857 = -1.538618516

Reorder the terms:
0.2857142857 + x = -1.538618516

Solving
0.2857142857 + x = -1.538618516

Solving for variable 'x'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + x = -1.538618516 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = -1.538618516 + -0.2857142857
x = -1.538618516 + -0.2857142857

Combine like terms: -1.538618516 + -0.2857142857 = -1.8243328017
x = -1.8243328017

Simplifying
x = -1.8243328017

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2529042303, -1.8243328017}