0.03x^2-33x+15000=7800

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Solution for 0.03x^2-33x+15000=7800 equation:


Simplifying
0.03x2 + -33x + 15000 = 7800

Reorder the terms:
15000 + -33x + 0.03x2 = 7800

Solving
15000 + -33x + 0.03x2 = 7800

Solving for variable 'x'.

Reorder the terms:
15000 + -7800 + -33x + 0.03x2 = 7800 + -7800

Combine like terms: 15000 + -7800 = 7200
7200 + -33x + 0.03x2 = 7800 + -7800

Combine like terms: 7800 + -7800 = 0
7200 + -33x + 0.03x2 = 0

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

Divide each side by '0.03'.
240000 + -1100x + x2 = 0

Move the constant term to the right:

Add '-240000' to each side of the equation.
240000 + -1100x + -240000 + x2 = 0 + -240000

Reorder the terms:
240000 + -240000 + -1100x + x2 = 0 + -240000

Combine like terms: 240000 + -240000 = 0
0 + -1100x + x2 = 0 + -240000
-1100x + x2 = 0 + -240000

Combine like terms: 0 + -240000 = -240000
-1100x + x2 = -240000

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 = -240000 + 302500

Reorder the terms:
302500 + -1100x + x2 = -240000 + 302500

Combine like terms: -240000 + 302500 = 62500
302500 + -1100x + x2 = 62500

Factor a perfect square on the left side:
(x + -550)(x + -550) = 62500

Calculate the square root of the right side: 250

Break this problem into two subproblems by setting 
(x + -550) equal to 250 and -250.

Subproblem 1

x + -550 = 250 Simplifying x + -550 = 250 Reorder the terms: -550 + x = 250 Solving -550 + x = 250 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 = 250 + 550 Combine like terms: -550 + 550 = 0 0 + x = 250 + 550 x = 250 + 550 Combine like terms: 250 + 550 = 800 x = 800 Simplifying x = 800

Subproblem 2

x + -550 = -250 Simplifying x + -550 = -250 Reorder the terms: -550 + x = -250 Solving -550 + x = -250 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 = -250 + 550 Combine like terms: -550 + 550 = 0 0 + x = -250 + 550 x = -250 + 550 Combine like terms: -250 + 550 = 300 x = 300 Simplifying x = 300

Solution

The solution to the problem is based on the solutions from the subproblems. x = {800, 300}

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