x^2+28x-20=0

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Solution for x^2+28x-20=0 equation: 


Simplifying
x2 + 28x + -20 = 0

Reorder the terms:
-20 + 28x + x2 = 0

Solving
-20 + 28x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 28x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 28x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 28x + x2 = 0 + 20
28x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
28x + x2 = 20

The x term is 28x.  Take half its coefficient (14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
28x + 196 + x2 = 20 + 196

Reorder the terms:
196 + 28x + x2 = 20 + 196

Combine like terms: 20 + 196 = 216
196 + 28x + x2 = 216

Factor a perfect square on the left side:
(x + 14)(x + 14) = 216

Calculate the square root of the right side: 14.696938457

Break this problem into two subproblems by setting 
(x + 14) equal to 14.696938457 and -14.696938457.


Subproblem 1
x + 14 = 14.696938457

Simplifying
x + 14 = 14.696938457

Reorder the terms:
14 + x = 14.696938457

Solving
14 + x = 14.696938457

Solving for variable 'x'.

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

Add '-14' to each side of the equation.
14 + -14 + x = 14.696938457 + -14

Combine like terms: 14 + -14 = 0
0 + x = 14.696938457 + -14
x = 14.696938457 + -14

Combine like terms: 14.696938457 + -14 = 0.696938457
x = 0.696938457

Simplifying
x = 0.696938457


Subproblem 2
x + 14 = -14.696938457

Simplifying
x + 14 = -14.696938457

Reorder the terms:
14 + x = -14.696938457

Solving
14 + x = -14.696938457

Solving for variable 'x'.

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

Add '-14' to each side of the equation.
14 + -14 + x = -14.696938457 + -14

Combine like terms: 14 + -14 = 0
0 + x = -14.696938457 + -14
x = -14.696938457 + -14

Combine like terms: -14.696938457 + -14 = -28.696938457
x = -28.696938457

Simplifying
x = -28.696938457


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.696938457, -28.696938457}

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