2x^2+29x+16=9

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Solution for 2x^2+29x+16=9 equation: 


Simplifying
2x2 + 29x + 16 = 9

Reorder the terms:
16 + 29x + 2x2 = 9

Solving
16 + 29x + 2x2 = 9

Solving for variable 'x'.

Reorder the terms:
16 + -9 + 29x + 2x2 = 9 + -9

Combine like terms: 16 + -9 = 7
7 + 29x + 2x2 = 9 + -9

Combine like terms: 9 + -9 = 0
7 + 29x + 2x2 = 0

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

Divide each side by '2'.
3.5 + 14.5x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 14.5x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 14.5x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 14.5x + x2 = 0 + -3.5
14.5x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
14.5x + x2 = -3.5

The x term is 14.5x.  Take half its coefficient (7.25).
Square it (52.5625) and add it to both sides.

Add '52.5625' to each side of the equation.
14.5x + 52.5625 + x2 = -3.5 + 52.5625

Reorder the terms:
52.5625 + 14.5x + x2 = -3.5 + 52.5625

Combine like terms: -3.5 + 52.5625 = 49.0625
52.5625 + 14.5x + x2 = 49.0625

Factor a perfect square on the left side:
(x + 7.25)(x + 7.25) = 49.0625

Calculate the square root of the right side: 7.004462863

Break this problem into two subproblems by setting 
(x + 7.25) equal to 7.004462863 and -7.004462863.


Subproblem 1
x + 7.25 = 7.004462863

Simplifying
x + 7.25 = 7.004462863

Reorder the terms:
7.25 + x = 7.004462863

Solving
7.25 + x = 7.004462863

Solving for variable 'x'.

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

Add '-7.25' to each side of the equation.
7.25 + -7.25 + x = 7.004462863 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + x = 7.004462863 + -7.25
x = 7.004462863 + -7.25

Combine like terms: 7.004462863 + -7.25 = -0.245537137
x = -0.245537137

Simplifying
x = -0.245537137


Subproblem 2
x + 7.25 = -7.004462863

Simplifying
x + 7.25 = -7.004462863

Reorder the terms:
7.25 + x = -7.004462863

Solving
7.25 + x = -7.004462863

Solving for variable 'x'.

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

Add '-7.25' to each side of the equation.
7.25 + -7.25 + x = -7.004462863 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + x = -7.004462863 + -7.25
x = -7.004462863 + -7.25

Combine like terms: -7.004462863 + -7.25 = -14.254462863
x = -14.254462863

Simplifying
x = -14.254462863


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.245537137, -14.254462863}

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