4x^2+62x+198=516

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Solution for 4x^2+62x+198=516 equation: 


Simplifying
4x2 + 62x + 198 = 516

Reorder the terms:
198 + 62x + 4x2 = 516

Solving
198 + 62x + 4x2 = 516

Solving for variable 'x'.

Reorder the terms:
198 + -516 + 62x + 4x2 = 516 + -516

Combine like terms: 198 + -516 = -318
-318 + 62x + 4x2 = 516 + -516

Combine like terms: 516 + -516 = 0
-318 + 62x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-159 + 31x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-159 + 31x + 2x2)' equal to zero and attempt to solve:

Simplifying
-159 + 31x + 2x2 = 0

Solving
-159 + 31x + 2x2 = 0

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

Divide each side by '2'.
-79.5 + 15.5x + x2 = 0

Move the constant term to the right:

Add '79.5' to each side of the equation.
-79.5 + 15.5x + 79.5 + x2 = 0 + 79.5

Reorder the terms:
-79.5 + 79.5 + 15.5x + x2 = 0 + 79.5

Combine like terms: -79.5 + 79.5 = 0.0
0.0 + 15.5x + x2 = 0 + 79.5
15.5x + x2 = 0 + 79.5

Combine like terms: 0 + 79.5 = 79.5
15.5x + x2 = 79.5

The x term is 15.5x.  Take half its coefficient (7.75).
Square it (60.0625) and add it to both sides.

Add '60.0625' to each side of the equation.
15.5x + 60.0625 + x2 = 79.5 + 60.0625

Reorder the terms:
60.0625 + 15.5x + x2 = 79.5 + 60.0625

Combine like terms: 79.5 + 60.0625 = 139.5625
60.0625 + 15.5x + x2 = 139.5625

Factor a perfect square on the left side:
(x + 7.75)(x + 7.75) = 139.5625

Calculate the square root of the right side: 11.813657351

Break this problem into two subproblems by setting 
(x + 7.75) equal to 11.813657351 and -11.813657351.


Subproblem 1
x + 7.75 = 11.813657351

Simplifying
x + 7.75 = 11.813657351

Reorder the terms:
7.75 + x = 11.813657351

Solving
7.75 + x = 11.813657351

Solving for variable 'x'.

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

Add '-7.75' to each side of the equation.
7.75 + -7.75 + x = 11.813657351 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + x = 11.813657351 + -7.75
x = 11.813657351 + -7.75

Combine like terms: 11.813657351 + -7.75 = 4.063657351
x = 4.063657351

Simplifying
x = 4.063657351


Subproblem 2
x + 7.75 = -11.813657351

Simplifying
x + 7.75 = -11.813657351

Reorder the terms:
7.75 + x = -11.813657351

Solving
7.75 + x = -11.813657351

Solving for variable 'x'.

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

Add '-7.75' to each side of the equation.
7.75 + -7.75 + x = -11.813657351 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + x = -11.813657351 + -7.75
x = -11.813657351 + -7.75

Combine like terms: -11.813657351 + -7.75 = -19.563657351
x = -19.563657351

Simplifying
x = -19.563657351


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.063657351, -19.563657351}
Solution
x = {4.063657351, -19.563657351}

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