-15x^2-44x+32=0

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Solution for -15x^2-44x+32=0 equation: 


Simplifying
-15x2 + -44x + 32 = 0

Reorder the terms:
32 + -44x + -15x2 = 0

Solving
32 + -44x + -15x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
-2.133333333 + 2.933333333x + x2 = 0

Move the constant term to the right:

Add '2.133333333' to each side of the equation.
-2.133333333 + 2.933333333x + 2.133333333 + x2 = 0 + 2.133333333

Reorder the terms:
-2.133333333 + 2.133333333 + 2.933333333x + x2 = 0 + 2.133333333

Combine like terms: -2.133333333 + 2.133333333 = 0.000000000
0.000000000 + 2.933333333x + x2 = 0 + 2.133333333
2.933333333x + x2 = 0 + 2.133333333

Combine like terms: 0 + 2.133333333 = 2.133333333
2.933333333x + x2 = 2.133333333

The x term is 2.933333333x.  Take half its coefficient (1.466666667).
Square it (2.151111112) and add it to both sides.

Add '2.151111112' to each side of the equation.
2.933333333x + 2.151111112 + x2 = 2.133333333 + 2.151111112

Reorder the terms:
2.151111112 + 2.933333333x + x2 = 2.133333333 + 2.151111112

Combine like terms: 2.133333333 + 2.151111112 = 4.284444445
2.151111112 + 2.933333333x + x2 = 4.284444445

Factor a perfect square on the left side:
(x + 1.466666667)(x + 1.466666667) = 4.284444445

Calculate the square root of the right side: 2.06988996

Break this problem into two subproblems by setting 
(x + 1.466666667) equal to 2.06988996 and -2.06988996.


Subproblem 1
x + 1.466666667 = 2.06988996

Simplifying
x + 1.466666667 = 2.06988996

Reorder the terms:
1.466666667 + x = 2.06988996

Solving
1.466666667 + x = 2.06988996

Solving for variable 'x'.

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

Add '-1.466666667' to each side of the equation.
1.466666667 + -1.466666667 + x = 2.06988996 + -1.466666667

Combine like terms: 1.466666667 + -1.466666667 = 0.000000000
0.000000000 + x = 2.06988996 + -1.466666667
x = 2.06988996 + -1.466666667

Combine like terms: 2.06988996 + -1.466666667 = 0.603223293
x = 0.603223293

Simplifying
x = 0.603223293


Subproblem 2
x + 1.466666667 = -2.06988996

Simplifying
x + 1.466666667 = -2.06988996

Reorder the terms:
1.466666667 + x = -2.06988996

Solving
1.466666667 + x = -2.06988996

Solving for variable 'x'.

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

Add '-1.466666667' to each side of the equation.
1.466666667 + -1.466666667 + x = -2.06988996 + -1.466666667

Combine like terms: 1.466666667 + -1.466666667 = 0.000000000
0.000000000 + x = -2.06988996 + -1.466666667
x = -2.06988996 + -1.466666667

Combine like terms: -2.06988996 + -1.466666667 = -3.536556627
x = -3.536556627

Simplifying
x = -3.536556627


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.603223293, -3.536556627}

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