2x^2+14x-1040=0

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Solution for 2x^2+14x-1040=0 equation: 


Simplifying
2x2 + 14x + -1040 = 0

Reorder the terms:
-1040 + 14x + 2x2 = 0

Solving
-1040 + 14x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-520 + 7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-520 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-520 + 7x + x2 = 0

Solving
-520 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '520' to each side of the equation.
-520 + 7x + 520 + x2 = 0 + 520

Reorder the terms:
-520 + 520 + 7x + x2 = 0 + 520

Combine like terms: -520 + 520 = 0
0 + 7x + x2 = 0 + 520
7x + x2 = 0 + 520

Combine like terms: 0 + 520 = 520
7x + x2 = 520

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 520 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 520 + 12.25

Combine like terms: 520 + 12.25 = 532.25
12.25 + 7x + x2 = 532.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 532.25

Calculate the square root of the right side: 23.07054399

Break this problem into two subproblems by setting 
(x + 3.5) equal to 23.07054399 and -23.07054399.


Subproblem 1
x + 3.5 = 23.07054399

Simplifying
x + 3.5 = 23.07054399

Reorder the terms:
3.5 + x = 23.07054399

Solving
3.5 + x = 23.07054399

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 23.07054399 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 23.07054399 + -3.5
x = 23.07054399 + -3.5

Combine like terms: 23.07054399 + -3.5 = 19.57054399
x = 19.57054399

Simplifying
x = 19.57054399


Subproblem 2
x + 3.5 = -23.07054399

Simplifying
x + 3.5 = -23.07054399

Reorder the terms:
3.5 + x = -23.07054399

Solving
3.5 + x = -23.07054399

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -23.07054399 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -23.07054399 + -3.5
x = -23.07054399 + -3.5

Combine like terms: -23.07054399 + -3.5 = -26.57054399
x = -26.57054399

Simplifying
x = -26.57054399


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.57054399, -26.57054399}
Solution
x = {19.57054399, -26.57054399}

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