16x^2+84x+62=120

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Solution for 16x^2+84x+62=120 equation: 


Simplifying
16x2 + 84x + 62 = 120

Reorder the terms:
62 + 84x + 16x2 = 120

Solving
62 + 84x + 16x2 = 120

Solving for variable 'x'.

Reorder the terms:
62 + -120 + 84x + 16x2 = 120 + -120

Combine like terms: 62 + -120 = -58
-58 + 84x + 16x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-58 + 84x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-29 + 42x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-29 + 42x + 8x2)' equal to zero and attempt to solve:

Simplifying
-29 + 42x + 8x2 = 0

Solving
-29 + 42x + 8x2 = 0

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

Divide each side by '8'.
-3.625 + 5.25x + x2 = 0

Move the constant term to the right:

Add '3.625' to each side of the equation.
-3.625 + 5.25x + 3.625 + x2 = 0 + 3.625

Reorder the terms:
-3.625 + 3.625 + 5.25x + x2 = 0 + 3.625

Combine like terms: -3.625 + 3.625 = 0.000
0.000 + 5.25x + x2 = 0 + 3.625
5.25x + x2 = 0 + 3.625

Combine like terms: 0 + 3.625 = 3.625
5.25x + x2 = 3.625

The x term is 5.25x.  Take half its coefficient (2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
5.25x + 6.890625 + x2 = 3.625 + 6.890625

Reorder the terms:
6.890625 + 5.25x + x2 = 3.625 + 6.890625

Combine like terms: 3.625 + 6.890625 = 10.515625
6.890625 + 5.25x + x2 = 10.515625

Factor a perfect square on the left side:
(x + 2.625)(x + 2.625) = 10.515625

Calculate the square root of the right side: 3.242780443

Break this problem into two subproblems by setting 
(x + 2.625) equal to 3.242780443 and -3.242780443.


Subproblem 1
x + 2.625 = 3.242780443

Simplifying
x + 2.625 = 3.242780443

Reorder the terms:
2.625 + x = 3.242780443

Solving
2.625 + x = 3.242780443

Solving for variable 'x'.

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

Add '-2.625' to each side of the equation.
2.625 + -2.625 + x = 3.242780443 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + x = 3.242780443 + -2.625
x = 3.242780443 + -2.625

Combine like terms: 3.242780443 + -2.625 = 0.617780443
x = 0.617780443

Simplifying
x = 0.617780443


Subproblem 2
x + 2.625 = -3.242780443

Simplifying
x + 2.625 = -3.242780443

Reorder the terms:
2.625 + x = -3.242780443

Solving
2.625 + x = -3.242780443

Solving for variable 'x'.

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

Add '-2.625' to each side of the equation.
2.625 + -2.625 + x = -3.242780443 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + x = -3.242780443 + -2.625
x = -3.242780443 + -2.625

Combine like terms: -3.242780443 + -2.625 = -5.867780443
x = -5.867780443

Simplifying
x = -5.867780443


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.617780443, -5.867780443}
Solution
x = {0.617780443, -5.867780443}

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