4x^2+148x-680=0

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Solution for 4x^2+148x-680=0 equation: 


Simplifying
4x2 + 148x + -680 = 0

Reorder the terms:
-680 + 148x + 4x2 = 0

Solving
-680 + 148x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-170 + 37x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-170 + 37x + x2)' equal to zero and attempt to solve:

Simplifying
-170 + 37x + x2 = 0

Solving
-170 + 37x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '170' to each side of the equation.
-170 + 37x + 170 + x2 = 0 + 170

Reorder the terms:
-170 + 170 + 37x + x2 = 0 + 170

Combine like terms: -170 + 170 = 0
0 + 37x + x2 = 0 + 170
37x + x2 = 0 + 170

Combine like terms: 0 + 170 = 170
37x + x2 = 170

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 = 170 + 342.25

Reorder the terms:
342.25 + 37x + x2 = 170 + 342.25

Combine like terms: 170 + 342.25 = 512.25
342.25 + 37x + x2 = 512.25

Factor a perfect square on the left side:
(x + 18.5)(x + 18.5) = 512.25

Calculate the square root of the right side: 22.632940596

Break this problem into two subproblems by setting 
(x + 18.5) equal to 22.632940596 and -22.632940596.


Subproblem 1
x + 18.5 = 22.632940596

Simplifying
x + 18.5 = 22.632940596

Reorder the terms:
18.5 + x = 22.632940596

Solving
18.5 + x = 22.632940596

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 = 22.632940596 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x = 22.632940596 + -18.5
x = 22.632940596 + -18.5

Combine like terms: 22.632940596 + -18.5 = 4.132940596
x = 4.132940596

Simplifying
x = 4.132940596


Subproblem 2
x + 18.5 = -22.632940596

Simplifying
x + 18.5 = -22.632940596

Reorder the terms:
18.5 + x = -22.632940596

Solving
18.5 + x = -22.632940596

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 = -22.632940596 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x = -22.632940596 + -18.5
x = -22.632940596 + -18.5

Combine like terms: -22.632940596 + -18.5 = -41.132940596
x = -41.132940596

Simplifying
x = -41.132940596


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.132940596, -41.132940596}
Solution
x = {4.132940596, -41.132940596}

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