0.03x^2-33x+7800=

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Solution for 0.03x^2-33x+7800= equation: 


Simplifying
0.03x2 + -33x + 7800 = 0

Reorder the terms:
7800 + -33x + 0.03x2 = 0

Solving
7800 + -33x + 0.03x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.03'.
260000 + -1100x + x2 = 0

Move the constant term to the right:

Add '-260000' to each side of the equation.
260000 + -1100x + -260000 + x2 = 0 + -260000

Reorder the terms:
260000 + -260000 + -1100x + x2 = 0 + -260000

Combine like terms: 260000 + -260000 = 0
0 + -1100x + x2 = 0 + -260000
-1100x + x2 = 0 + -260000

Combine like terms: 0 + -260000 = -260000
-1100x + x2 = -260000

The x term is -1100x.  Take half its coefficient (-550).
Square it (302500) and add it to both sides.

Add '302500' to each side of the equation.
-1100x + 302500 + x2 = -260000 + 302500

Reorder the terms:
302500 + -1100x + x2 = -260000 + 302500

Combine like terms: -260000 + 302500 = 42500
302500 + -1100x + x2 = 42500

Factor a perfect square on the left side:
(x + -550)(x + -550) = 42500

Calculate the square root of the right side: 206.155281281

Break this problem into two subproblems by setting 
(x + -550) equal to 206.155281281 and -206.155281281.


Subproblem 1
x + -550 = 206.155281281

Simplifying
x + -550 = 206.155281281

Reorder the terms:
-550 + x = 206.155281281

Solving
-550 + x = 206.155281281

Solving for variable 'x'.

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

Add '550' to each side of the equation.
-550 + 550 + x = 206.155281281 + 550

Combine like terms: -550 + 550 = 0
0 + x = 206.155281281 + 550
x = 206.155281281 + 550

Combine like terms: 206.155281281 + 550 = 756.155281281
x = 756.155281281

Simplifying
x = 756.155281281


Subproblem 2
x + -550 = -206.155281281

Simplifying
x + -550 = -206.155281281

Reorder the terms:
-550 + x = -206.155281281

Solving
-550 + x = -206.155281281

Solving for variable 'x'.

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

Add '550' to each side of the equation.
-550 + 550 + x = -206.155281281 + 550

Combine like terms: -550 + 550 = 0
0 + x = -206.155281281 + 550
x = -206.155281281 + 550

Combine like terms: -206.155281281 + 550 = 343.844718719
x = 343.844718719

Simplifying
x = 343.844718719


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {756.155281281, 343.844718719}

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