16x^2+158x+40=0

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Solution for 16x^2+158x+40=0 equation: 


Simplifying
16x2 + 158x + 40 = 0

Reorder the terms:
40 + 158x + 16x2 = 0

Solving
40 + 158x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + 79x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(20 + 79x + 8x2)' equal to zero and attempt to solve:

Simplifying
20 + 79x + 8x2 = 0

Solving
20 + 79x + 8x2 = 0

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

Divide each side by '8'.
2.5 + 9.875x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 9.875x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 9.875x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 9.875x + x2 = 0 + -2.5
9.875x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
9.875x + x2 = -2.5

The x term is 9.875x.  Take half its coefficient (4.9375).
Square it (24.37890625) and add it to both sides.

Add '24.37890625' to each side of the equation.
9.875x + 24.37890625 + x2 = -2.5 + 24.37890625

Reorder the terms:
24.37890625 + 9.875x + x2 = -2.5 + 24.37890625

Combine like terms: -2.5 + 24.37890625 = 21.87890625
24.37890625 + 9.875x + x2 = 21.87890625

Factor a perfect square on the left side:
(x + 4.9375)(x + 4.9375) = 21.87890625

Calculate the square root of the right side: 4.677489311

Break this problem into two subproblems by setting 
(x + 4.9375) equal to 4.677489311 and -4.677489311.


Subproblem 1
x + 4.9375 = 4.677489311

Simplifying
x + 4.9375 = 4.677489311

Reorder the terms:
4.9375 + x = 4.677489311

Solving
4.9375 + x = 4.677489311

Solving for variable 'x'.

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

Add '-4.9375' to each side of the equation.
4.9375 + -4.9375 + x = 4.677489311 + -4.9375

Combine like terms: 4.9375 + -4.9375 = 0.0000
0.0000 + x = 4.677489311 + -4.9375
x = 4.677489311 + -4.9375

Combine like terms: 4.677489311 + -4.9375 = -0.260010689
x = -0.260010689

Simplifying
x = -0.260010689


Subproblem 2
x + 4.9375 = -4.677489311

Simplifying
x + 4.9375 = -4.677489311

Reorder the terms:
4.9375 + x = -4.677489311

Solving
4.9375 + x = -4.677489311

Solving for variable 'x'.

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

Add '-4.9375' to each side of the equation.
4.9375 + -4.9375 + x = -4.677489311 + -4.9375

Combine like terms: 4.9375 + -4.9375 = 0.0000
0.0000 + x = -4.677489311 + -4.9375
x = -4.677489311 + -4.9375

Combine like terms: -4.677489311 + -4.9375 = -9.614989311
x = -9.614989311

Simplifying
x = -9.614989311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.260010689, -9.614989311}
Solution
x = {-0.260010689, -9.614989311}

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