2x^2+28x-1004=0

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Solution for 2x^2+28x-1004=0 equation: 


Simplifying
2x2 + 28x + -1004 = 0

Reorder the terms:
-1004 + 28x + 2x2 = 0

Solving
-1004 + 28x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-502 + 14x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-502 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
-502 + 14x + x2 = 0

Solving
-502 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '502' to each side of the equation.
-502 + 14x + 502 + x2 = 0 + 502

Reorder the terms:
-502 + 502 + 14x + x2 = 0 + 502

Combine like terms: -502 + 502 = 0
0 + 14x + x2 = 0 + 502
14x + x2 = 0 + 502

Combine like terms: 0 + 502 = 502
14x + x2 = 502

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 502 + 49

Reorder the terms:
49 + 14x + x2 = 502 + 49

Combine like terms: 502 + 49 = 551
49 + 14x + x2 = 551

Factor a perfect square on the left side:
(x + 7)(x + 7) = 551

Calculate the square root of the right side: 23.473389189

Break this problem into two subproblems by setting 
(x + 7) equal to 23.473389189 and -23.473389189.


Subproblem 1
x + 7 = 23.473389189

Simplifying
x + 7 = 23.473389189

Reorder the terms:
7 + x = 23.473389189

Solving
7 + x = 23.473389189

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 23.473389189 + -7

Combine like terms: 7 + -7 = 0
0 + x = 23.473389189 + -7
x = 23.473389189 + -7

Combine like terms: 23.473389189 + -7 = 16.473389189
x = 16.473389189

Simplifying
x = 16.473389189


Subproblem 2
x + 7 = -23.473389189

Simplifying
x + 7 = -23.473389189

Reorder the terms:
7 + x = -23.473389189

Solving
7 + x = -23.473389189

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -23.473389189 + -7

Combine like terms: 7 + -7 = 0
0 + x = -23.473389189 + -7
x = -23.473389189 + -7

Combine like terms: -23.473389189 + -7 = -30.473389189
x = -30.473389189

Simplifying
x = -30.473389189


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.473389189, -30.473389189}
Solution
x = {16.473389189, -30.473389189}

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