2(2x^2+7x-183)=0

Solution for 2(2x^2+7x-183)=0 equation:

Simplifying
2(2x2 + 7x + -183) = 0

Reorder the terms:
2(-183 + 7x + 2x2) = 0
(-183 * 2 + 7x * 2 + 2x2 * 2) = 0
(-366 + 14x + 4x2) = 0

Solving
-366 + 14x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-183 + 7x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-183 + 7x + 2x2)' equal to zero and attempt to solve:

Simplifying
-183 + 7x + 2x2 = 0

Solving
-183 + 7x + 2x2 = 0

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

Divide each side by '2'.
-91.5 + 3.5x + x2 = 0

Move the constant term to the right:

Add '91.5' to each side of the equation.
-91.5 + 3.5x + 91.5 + x2 = 0 + 91.5

Reorder the terms:
-91.5 + 91.5 + 3.5x + x2 = 0 + 91.5

Combine like terms: -91.5 + 91.5 = 0.0
0.0 + 3.5x + x2 = 0 + 91.5
3.5x + x2 = 0 + 91.5

Combine like terms: 0 + 91.5 = 91.5
3.5x + x2 = 91.5

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 91.5 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 91.5 + 3.0625

Combine like terms: 91.5 + 3.0625 = 94.5625
3.0625 + 3.5x + x2 = 94.5625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 94.5625

Calculate the square root of the right side: 9.724325169

Break this problem into two subproblems by setting 
(x + 1.75) equal to 9.724325169 and -9.724325169.

Subproblem 1
x + 1.75 = 9.724325169

Simplifying
x + 1.75 = 9.724325169

Reorder the terms:
1.75 + x = 9.724325169

Solving
1.75 + x = 9.724325169

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 9.724325169 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 9.724325169 + -1.75
x = 9.724325169 + -1.75

Combine like terms: 9.724325169 + -1.75 = 7.974325169
x = 7.974325169

Simplifying
x = 7.974325169

Subproblem 2
x + 1.75 = -9.724325169

Simplifying
x + 1.75 = -9.724325169

Reorder the terms:
1.75 + x = -9.724325169

Solving
1.75 + x = -9.724325169

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -9.724325169 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -9.724325169 + -1.75
x = -9.724325169 + -1.75

Combine like terms: -9.724325169 + -1.75 = -11.474325169
x = -11.474325169

Simplifying
x = -11.474325169

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.974325169, -11.474325169}
Solution
x = {7.974325169, -11.474325169}