.08x+.06x(x+9)=1.24

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Solution for .08x+.06x(x+9)=1.24 equation: 


Simplifying
0.08x + 0.06x(x + 9) = 1.24

Reorder the terms:
0.08x + 0.06x(9 + x) = 1.24
0.08x + (9 * 0.06x + x * 0.06x) = 1.24
0.08x + (0.54x + 0.06x2) = 1.24

Combine like terms: 0.08x + 0.54x = 0.62x
0.62x + 0.06x2 = 1.24

Solving
0.62x + 0.06x2 = 1.24

Solving for variable 'x'.

Reorder the terms:
-1.24 + 0.62x + 0.06x2 = 1.24 + -1.24

Combine like terms: 1.24 + -1.24 = 0.00
-1.24 + 0.62x + 0.06x2 = 0.00

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

Divide each side by '0.06'.
-20.66666667 + 10.33333333x + x2 = 0

Move the constant term to the right:

Add '20.66666667' to each side of the equation.
-20.66666667 + 10.33333333x + 20.66666667 + x2 = 0 + 20.66666667

Reorder the terms:
-20.66666667 + 20.66666667 + 10.33333333x + x2 = 0 + 20.66666667

Combine like terms: -20.66666667 + 20.66666667 = 0.00000000
0.00000000 + 10.33333333x + x2 = 0 + 20.66666667
10.33333333x + x2 = 0 + 20.66666667

Combine like terms: 0 + 20.66666667 = 20.66666667
10.33333333x + x2 = 20.66666667

The x term is 10.33333333x.  Take half its coefficient (5.166666665).
Square it (26.69444443) and add it to both sides.

Add '26.69444443' to each side of the equation.
10.33333333x + 26.69444443 + x2 = 20.66666667 + 26.69444443

Reorder the terms:
26.69444443 + 10.33333333x + x2 = 20.66666667 + 26.69444443

Combine like terms: 20.66666667 + 26.69444443 = 47.3611111
26.69444443 + 10.33333333x + x2 = 47.3611111

Factor a perfect square on the left side:
(x + 5.166666665)(x + 5.166666665) = 47.3611111

Calculate the square root of the right side: 6.88194094

Break this problem into two subproblems by setting 
(x + 5.166666665) equal to 6.88194094 and -6.88194094.


Subproblem 1
x + 5.166666665 = 6.88194094

Simplifying
x + 5.166666665 = 6.88194094

Reorder the terms:
5.166666665 + x = 6.88194094

Solving
5.166666665 + x = 6.88194094

Solving for variable 'x'.

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

Add '-5.166666665' to each side of the equation.
5.166666665 + -5.166666665 + x = 6.88194094 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = 6.88194094 + -5.166666665
x = 6.88194094 + -5.166666665

Combine like terms: 6.88194094 + -5.166666665 = 1.715274275
x = 1.715274275

Simplifying
x = 1.715274275


Subproblem 2
x + 5.166666665 = -6.88194094

Simplifying
x + 5.166666665 = -6.88194094

Reorder the terms:
5.166666665 + x = -6.88194094

Solving
5.166666665 + x = -6.88194094

Solving for variable 'x'.

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

Add '-5.166666665' to each side of the equation.
5.166666665 + -5.166666665 + x = -6.88194094 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = -6.88194094 + -5.166666665
x = -6.88194094 + -5.166666665

Combine like terms: -6.88194094 + -5.166666665 = -12.048607605
x = -12.048607605

Simplifying
x = -12.048607605


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.715274275, -12.048607605}

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