9x^2+48x+52=0

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Solution for 9x^2+48x+52=0 equation: 


Simplifying
9x2 + 48x + 52 = 0

Reorder the terms:
52 + 48x + 9x2 = 0

Solving
52 + 48x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
5.777777778 + 5.333333333x + x2 = 0

Move the constant term to the right:

Add '-5.777777778' to each side of the equation.
5.777777778 + 5.333333333x + -5.777777778 + x2 = 0 + -5.777777778

Reorder the terms:
5.777777778 + -5.777777778 + 5.333333333x + x2 = 0 + -5.777777778

Combine like terms: 5.777777778 + -5.777777778 = 0.000000000
0.000000000 + 5.333333333x + x2 = 0 + -5.777777778
5.333333333x + x2 = 0 + -5.777777778

Combine like terms: 0 + -5.777777778 = -5.777777778
5.333333333x + x2 = -5.777777778

The x term is 5.333333333x.  Take half its coefficient (2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
5.333333333x + 7.111111113 + x2 = -5.777777778 + 7.111111113

Reorder the terms:
7.111111113 + 5.333333333x + x2 = -5.777777778 + 7.111111113

Combine like terms: -5.777777778 + 7.111111113 = 1.333333335
7.111111113 + 5.333333333x + x2 = 1.333333335

Factor a perfect square on the left side:
(x + 2.666666667)(x + 2.666666667) = 1.333333335

Calculate the square root of the right side: 1.154700539

Break this problem into two subproblems by setting 
(x + 2.666666667) equal to 1.154700539 and -1.154700539.


Subproblem 1
x + 2.666666667 = 1.154700539

Simplifying
x + 2.666666667 = 1.154700539

Reorder the terms:
2.666666667 + x = 1.154700539

Solving
2.666666667 + x = 1.154700539

Solving for variable 'x'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + x = 1.154700539 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + x = 1.154700539 + -2.666666667
x = 1.154700539 + -2.666666667

Combine like terms: 1.154700539 + -2.666666667 = -1.511966128
x = -1.511966128

Simplifying
x = -1.511966128


Subproblem 2
x + 2.666666667 = -1.154700539

Simplifying
x + 2.666666667 = -1.154700539

Reorder the terms:
2.666666667 + x = -1.154700539

Solving
2.666666667 + x = -1.154700539

Solving for variable 'x'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + x = -1.154700539 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + x = -1.154700539 + -2.666666667
x = -1.154700539 + -2.666666667

Combine like terms: -1.154700539 + -2.666666667 = -3.821367206
x = -3.821367206

Simplifying
x = -3.821367206


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.511966128, -3.821367206}

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