2x^2+14x-584=0

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Solution for 2x^2+14x-584=0 equation: 


Simplifying
2x2 + 14x + -584 = 0

Reorder the terms:
-584 + 14x + 2x2 = 0

Solving
-584 + 14x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-292 + 7x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-292 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-292 + 7x + x2 = 0

Solving
-292 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '292' to each side of the equation.
-292 + 7x + 292 + x2 = 0 + 292

Reorder the terms:
-292 + 292 + 7x + x2 = 0 + 292

Combine like terms: -292 + 292 = 0
0 + 7x + x2 = 0 + 292
7x + x2 = 0 + 292

Combine like terms: 0 + 292 = 292
7x + x2 = 292

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 = 292 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 292 + 12.25

Combine like terms: 292 + 12.25 = 304.25
12.25 + 7x + x2 = 304.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 304.25

Calculate the square root of the right side: 17.442763543

Break this problem into two subproblems by setting 
(x + 3.5) equal to 17.442763543 and -17.442763543.


Subproblem 1
x + 3.5 = 17.442763543

Simplifying
x + 3.5 = 17.442763543

Reorder the terms:
3.5 + x = 17.442763543

Solving
3.5 + x = 17.442763543

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 = 17.442763543 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 17.442763543 + -3.5
x = 17.442763543 + -3.5

Combine like terms: 17.442763543 + -3.5 = 13.942763543
x = 13.942763543

Simplifying
x = 13.942763543


Subproblem 2
x + 3.5 = -17.442763543

Simplifying
x + 3.5 = -17.442763543

Reorder the terms:
3.5 + x = -17.442763543

Solving
3.5 + x = -17.442763543

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 = -17.442763543 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -17.442763543 + -3.5
x = -17.442763543 + -3.5

Combine like terms: -17.442763543 + -3.5 = -20.942763543
x = -20.942763543

Simplifying
x = -20.942763543


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.942763543, -20.942763543}
Solution
x = {13.942763543, -20.942763543}

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