0.0075x^2-14x+1200=0

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Solution for 0.0075x^2-14x+1200=0 equation: 


Simplifying
0.0075x2 + -14x + 1200 = 0

Reorder the terms:
1200 + -14x + 0.0075x2 = 0

Solving
1200 + -14x + 0.0075x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.0075 the coefficient of the squared term: 

Divide each side by '0.0075'.
160000 + -1866.666667x + x2 = 0

Move the constant term to the right:

Add '-160000' to each side of the equation.
160000 + -1866.666667x + -160000 + x2 = 0 + -160000

Reorder the terms:
160000 + -160000 + -1866.666667x + x2 = 0 + -160000

Combine like terms: 160000 + -160000 = 0
0 + -1866.666667x + x2 = 0 + -160000
-1866.666667x + x2 = 0 + -160000

Combine like terms: 0 + -160000 = -160000
-1866.666667x + x2 = -160000

The x term is -1866.666667x.  Take half its coefficient (-933.3333335).
Square it (871111.1114) and add it to both sides.

Add '871111.1114' to each side of the equation.
-1866.666667x + 871111.1114 + x2 = -160000 + 871111.1114

Reorder the terms:
871111.1114 + -1866.666667x + x2 = -160000 + 871111.1114

Combine like terms: -160000 + 871111.1114 = 711111.1114
871111.1114 + -1866.666667x + x2 = 711111.1114

Factor a perfect square on the left side:
(x + -933.3333335)(x + -933.3333335) = 711111.1114

Calculate the square root of the right side: 843.274042883

Break this problem into two subproblems by setting 
(x + -933.3333335) equal to 843.274042883 and -843.274042883.


Subproblem 1
x + -933.3333335 = 843.274042883

Simplifying
x + -933.3333335 = 843.274042883

Reorder the terms:
-933.3333335 + x = 843.274042883

Solving
-933.3333335 + x = 843.274042883

Solving for variable 'x'.

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

Add '933.3333335' to each side of the equation.
-933.3333335 + 933.3333335 + x = 843.274042883 + 933.3333335

Combine like terms: -933.3333335 + 933.3333335 = 0.0000000
0.0000000 + x = 843.274042883 + 933.3333335
x = 843.274042883 + 933.3333335

Combine like terms: 843.274042883 + 933.3333335 = 1776.607376383
x = 1776.607376383

Simplifying
x = 1776.607376383


Subproblem 2
x + -933.3333335 = -843.274042883

Simplifying
x + -933.3333335 = -843.274042883

Reorder the terms:
-933.3333335 + x = -843.274042883

Solving
-933.3333335 + x = -843.274042883

Solving for variable 'x'.

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

Add '933.3333335' to each side of the equation.
-933.3333335 + 933.3333335 + x = -843.274042883 + 933.3333335

Combine like terms: -933.3333335 + 933.3333335 = 0.0000000
0.0000000 + x = -843.274042883 + 933.3333335
x = -843.274042883 + 933.3333335

Combine like terms: -843.274042883 + 933.3333335 = 90.059290617
x = 90.059290617

Simplifying
x = 90.059290617


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1776.607376383, 90.059290617}

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