.3x^2-45x-1000=0

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Solution for .3x^2-45x-1000=0 equation: 


Simplifying
0.3x2 + -45x + -1000 = 0

Reorder the terms:
-1000 + -45x + 0.3x2 = 0

Solving
-1000 + -45x + 0.3x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.3'.
-3333.333333 + -150x + x2 = 0

Move the constant term to the right:

Add '3333.333333' to each side of the equation.
-3333.333333 + -150x + 3333.333333 + x2 = 0 + 3333.333333

Reorder the terms:
-3333.333333 + 3333.333333 + -150x + x2 = 0 + 3333.333333

Combine like terms: -3333.333333 + 3333.333333 = 0.000000
0.000000 + -150x + x2 = 0 + 3333.333333
-150x + x2 = 0 + 3333.333333

Combine like terms: 0 + 3333.333333 = 3333.333333
-150x + x2 = 3333.333333

The x term is -150x.  Take half its coefficient (-75).
Square it (5625) and add it to both sides.

Add '5625' to each side of the equation.
-150x + 5625 + x2 = 3333.333333 + 5625

Reorder the terms:
5625 + -150x + x2 = 3333.333333 + 5625

Combine like terms: 3333.333333 + 5625 = 8958.333333
5625 + -150x + x2 = 8958.333333

Factor a perfect square on the left side:
(x + -75)(x + -75) = 8958.333333

Calculate the square root of the right side: 94.648472428

Break this problem into two subproblems by setting 
(x + -75) equal to 94.648472428 and -94.648472428.


Subproblem 1
x + -75 = 94.648472428

Simplifying
x + -75 = 94.648472428

Reorder the terms:
-75 + x = 94.648472428

Solving
-75 + x = 94.648472428

Solving for variable 'x'.

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

Add '75' to each side of the equation.
-75 + 75 + x = 94.648472428 + 75

Combine like terms: -75 + 75 = 0
0 + x = 94.648472428 + 75
x = 94.648472428 + 75

Combine like terms: 94.648472428 + 75 = 169.648472428
x = 169.648472428

Simplifying
x = 169.648472428


Subproblem 2
x + -75 = -94.648472428

Simplifying
x + -75 = -94.648472428

Reorder the terms:
-75 + x = -94.648472428

Solving
-75 + x = -94.648472428

Solving for variable 'x'.

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

Add '75' to each side of the equation.
-75 + 75 + x = -94.648472428 + 75

Combine like terms: -75 + 75 = 0
0 + x = -94.648472428 + 75
x = -94.648472428 + 75

Combine like terms: -94.648472428 + 75 = -19.648472428
x = -19.648472428

Simplifying
x = -19.648472428


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {169.648472428, -19.648472428}

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