x^2+5.25x=0.66

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Solution for x^2+5.25x=0.66 equation: 


Simplifying
x2 + 5.25x = 0.66

Reorder the terms:
5.25x + x2 = 0.66

Solving
5.25x + x2 = 0.66

Solving for variable 'x'.

Reorder the terms:
-0.66 + 5.25x + x2 = 0.66 + -0.66

Combine like terms: 0.66 + -0.66 = 0.00
-0.66 + 5.25x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.66' to each side of the equation.
-0.66 + 5.25x + 0.66 + x2 = 0.00 + 0.66

Reorder the terms:
-0.66 + 0.66 + 5.25x + x2 = 0.00 + 0.66

Combine like terms: -0.66 + 0.66 = 0.00
0.00 + 5.25x + x2 = 0.00 + 0.66
5.25x + x2 = 0.00 + 0.66

Combine like terms: 0.00 + 0.66 = 0.66
5.25x + x2 = 0.66

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 = 0.66 + 6.890625

Reorder the terms:
6.890625 + 5.25x + x2 = 0.66 + 6.890625

Combine like terms: 0.66 + 6.890625 = 7.550625
6.890625 + 5.25x + x2 = 7.550625

Factor a perfect square on the left side:
(x + 2.625)(x + 2.625) = 7.550625

Calculate the square root of the right side: 2.747840061

Break this problem into two subproblems by setting 
(x + 2.625) equal to 2.747840061 and -2.747840061.


Subproblem 1
x + 2.625 = 2.747840061

Simplifying
x + 2.625 = 2.747840061

Reorder the terms:
2.625 + x = 2.747840061

Solving
2.625 + x = 2.747840061

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 = 2.747840061 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + x = 2.747840061 + -2.625
x = 2.747840061 + -2.625

Combine like terms: 2.747840061 + -2.625 = 0.122840061
x = 0.122840061

Simplifying
x = 0.122840061


Subproblem 2
x + 2.625 = -2.747840061

Simplifying
x + 2.625 = -2.747840061

Reorder the terms:
2.625 + x = -2.747840061

Solving
2.625 + x = -2.747840061

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 = -2.747840061 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + x = -2.747840061 + -2.625
x = -2.747840061 + -2.625

Combine like terms: -2.747840061 + -2.625 = -5.372840061
x = -5.372840061

Simplifying
x = -5.372840061


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.122840061, -5.372840061}

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