2x^2+74x-1156=0

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Solution for 2x^2+74x-1156=0 equation: 


Simplifying
2x2 + 74x + -1156 = 0

Reorder the terms:
-1156 + 74x + 2x2 = 0

Solving
-1156 + 74x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-578 + 37x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-578 + 37x + x2)' equal to zero and attempt to solve:

Simplifying
-578 + 37x + x2 = 0

Solving
-578 + 37x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '578' to each side of the equation.
-578 + 37x + 578 + x2 = 0 + 578

Reorder the terms:
-578 + 578 + 37x + x2 = 0 + 578

Combine like terms: -578 + 578 = 0
0 + 37x + x2 = 0 + 578
37x + x2 = 0 + 578

Combine like terms: 0 + 578 = 578
37x + x2 = 578

The x term is 37x.  Take half its coefficient (18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
37x + 342.25 + x2 = 578 + 342.25

Reorder the terms:
342.25 + 37x + x2 = 578 + 342.25

Combine like terms: 578 + 342.25 = 920.25
342.25 + 37x + x2 = 920.25

Factor a perfect square on the left side:
(x + 18.5)(x + 18.5) = 920.25

Calculate the square root of the right side: 30.335622624

Break this problem into two subproblems by setting 
(x + 18.5) equal to 30.335622624 and -30.335622624.


Subproblem 1
x + 18.5 = 30.335622624

Simplifying
x + 18.5 = 30.335622624

Reorder the terms:
18.5 + x = 30.335622624

Solving
18.5 + x = 30.335622624

Solving for variable 'x'.

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

Add '-18.5' to each side of the equation.
18.5 + -18.5 + x = 30.335622624 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x = 30.335622624 + -18.5
x = 30.335622624 + -18.5

Combine like terms: 30.335622624 + -18.5 = 11.835622624
x = 11.835622624

Simplifying
x = 11.835622624


Subproblem 2
x + 18.5 = -30.335622624

Simplifying
x + 18.5 = -30.335622624

Reorder the terms:
18.5 + x = -30.335622624

Solving
18.5 + x = -30.335622624

Solving for variable 'x'.

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

Add '-18.5' to each side of the equation.
18.5 + -18.5 + x = -30.335622624 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x = -30.335622624 + -18.5
x = -30.335622624 + -18.5

Combine like terms: -30.335622624 + -18.5 = -48.835622624
x = -48.835622624

Simplifying
x = -48.835622624


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.835622624, -48.835622624}
Solution
x = {11.835622624, -48.835622624}

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