1.5=-0.00009x^2+0.0299x+1.3005

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Solution for 1.5=-0.00009x^2+0.0299x+1.3005 equation: 


Simplifying
1.5 = -0.00009x2 + 0.0299x + 1.3005

Reorder the terms:
1.5 = 1.3005 + 0.0299x + -0.00009x2

Solving
1.5 = 1.3005 + 0.0299x + -0.00009x2

Solving for variable 'x'.

Combine like terms: 1.5 + -1.3005 = 0.1995
0.1995 + -0.0299x + 0.00009x2 = 1.3005 + 0.0299x + -0.00009x2 + -1.3005 + -0.0299x + 0.00009x2

Reorder the terms:
0.1995 + -0.0299x + 0.00009x2 = 1.3005 + -1.3005 + 0.0299x + -0.0299x + -0.00009x2 + 0.00009x2

Combine like terms: 1.3005 + -1.3005 = 0.0000
0.1995 + -0.0299x + 0.00009x2 = 0.0000 + 0.0299x + -0.0299x + -0.00009x2 + 0.00009x2
0.1995 + -0.0299x + 0.00009x2 = 0.0299x + -0.0299x + -0.00009x2 + 0.00009x2

Combine like terms: 0.0299x + -0.0299x = 0.0000
0.1995 + -0.0299x + 0.00009x2 = 0.0000 + -0.00009x2 + 0.00009x2
0.1995 + -0.0299x + 0.00009x2 = -0.00009x2 + 0.00009x2

Combine like terms: -0.00009x2 + 0.00009x2 = 0.00000
0.1995 + -0.0299x + 0.00009x2 = 0.00000

Begin completing the square.  Divide all terms by
0.00009 the coefficient of the squared term: 

Divide each side by '0.00009'.
2216.666667 + -332.2222222x + x2 = 0

Move the constant term to the right:

Add '-2216.666667' to each side of the equation.
2216.666667 + -332.2222222x + -2216.666667 + x2 = 0 + -2216.666667

Reorder the terms:
2216.666667 + -2216.666667 + -332.2222222x + x2 = 0 + -2216.666667

Combine like terms: 2216.666667 + -2216.666667 = 0.000000
0.000000 + -332.2222222x + x2 = 0 + -2216.666667
-332.2222222x + x2 = 0 + -2216.666667

Combine like terms: 0 + -2216.666667 = -2216.666667
-332.2222222x + x2 = -2216.666667

The x term is -332.2222222x.  Take half its coefficient (-166.1111111).
Square it (27592.90123) and add it to both sides.

Add '27592.90123' to each side of the equation.
-332.2222222x + 27592.90123 + x2 = -2216.666667 + 27592.90123

Reorder the terms:
27592.90123 + -332.2222222x + x2 = -2216.666667 + 27592.90123

Combine like terms: -2216.666667 + 27592.90123 = 25376.234563
27592.90123 + -332.2222222x + x2 = 25376.234563

Factor a perfect square on the left side:
(x + -166.1111111)(x + -166.1111111) = 25376.234563

Calculate the square root of the right side: 159.29919825

Break this problem into two subproblems by setting 
(x + -166.1111111) equal to 159.29919825 and -159.29919825.


Subproblem 1
x + -166.1111111 = 159.29919825

Simplifying
x + -166.1111111 = 159.29919825

Reorder the terms:
-166.1111111 + x = 159.29919825

Solving
-166.1111111 + x = 159.29919825

Solving for variable 'x'.

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

Add '166.1111111' to each side of the equation.
-166.1111111 + 166.1111111 + x = 159.29919825 + 166.1111111

Combine like terms: -166.1111111 + 166.1111111 = 0.0000000
0.0000000 + x = 159.29919825 + 166.1111111
x = 159.29919825 + 166.1111111

Combine like terms: 159.29919825 + 166.1111111 = 325.41030935
x = 325.41030935

Simplifying
x = 325.41030935


Subproblem 2
x + -166.1111111 = -159.29919825

Simplifying
x + -166.1111111 = -159.29919825

Reorder the terms:
-166.1111111 + x = -159.29919825

Solving
-166.1111111 + x = -159.29919825

Solving for variable 'x'.

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

Add '166.1111111' to each side of the equation.
-166.1111111 + 166.1111111 + x = -159.29919825 + 166.1111111

Combine like terms: -166.1111111 + 166.1111111 = 0.0000000
0.0000000 + x = -159.29919825 + 166.1111111
x = -159.29919825 + 166.1111111

Combine like terms: -159.29919825 + 166.1111111 = 6.81191285
x = 6.81191285

Simplifying
x = 6.81191285


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {325.41030935, 6.81191285}

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