0.15-0.0075x-x^2=0

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Solution for 0.15-0.0075x-x^2=0 equation: 


Simplifying
0.15 + -0.0075x + -1x2 = 0

Solving
0.15 + -0.0075x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.15 + 0.0075x + x2 = 0

Move the constant term to the right:

Add '0.15' to each side of the equation.
-0.15 + 0.0075x + 0.15 + x2 = 0 + 0.15

Reorder the terms:
-0.15 + 0.15 + 0.0075x + x2 = 0 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + 0.0075x + x2 = 0 + 0.15
0.0075x + x2 = 0 + 0.15

Combine like terms: 0 + 0.15 = 0.15
0.0075x + x2 = 0.15

The x term is 0.0075x.  Take half its coefficient (0.00375).
Square it (0.0000140625) and add it to both sides.

Add '0.0000140625' to each side of the equation.
0.0075x + 0.0000140625 + x2 = 0.15 + 0.0000140625

Reorder the terms:
0.0000140625 + 0.0075x + x2 = 0.15 + 0.0000140625

Combine like terms: 0.15 + 0.0000140625 = 0.1500140625
0.0000140625 + 0.0075x + x2 = 0.1500140625

Factor a perfect square on the left side:
(x + 0.00375)(x + 0.00375) = 0.1500140625

Calculate the square root of the right side: 0.387316489

Break this problem into two subproblems by setting 
(x + 0.00375) equal to 0.387316489 and -0.387316489.


Subproblem 1
x + 0.00375 = 0.387316489

Simplifying
x + 0.00375 = 0.387316489

Reorder the terms:
0.00375 + x = 0.387316489

Solving
0.00375 + x = 0.387316489

Solving for variable 'x'.

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

Add '-0.00375' to each side of the equation.
0.00375 + -0.00375 + x = 0.387316489 + -0.00375

Combine like terms: 0.00375 + -0.00375 = 0.00000
0.00000 + x = 0.387316489 + -0.00375
x = 0.387316489 + -0.00375

Combine like terms: 0.387316489 + -0.00375 = 0.383566489
x = 0.383566489

Simplifying
x = 0.383566489


Subproblem 2
x + 0.00375 = -0.387316489

Simplifying
x + 0.00375 = -0.387316489

Reorder the terms:
0.00375 + x = -0.387316489

Solving
0.00375 + x = -0.387316489

Solving for variable 'x'.

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

Add '-0.00375' to each side of the equation.
0.00375 + -0.00375 + x = -0.387316489 + -0.00375

Combine like terms: 0.00375 + -0.00375 = 0.00000
0.00000 + x = -0.387316489 + -0.00375
x = -0.387316489 + -0.00375

Combine like terms: -0.387316489 + -0.00375 = -0.391066489
x = -0.391066489

Simplifying
x = -0.391066489


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.383566489, -0.391066489}

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