2x*x-3x=126000

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Solution for 2x*x-3x=126000 equation:


Simplifying
2x * x + -3x = 126000

Multiply x * x
2x2 + -3x = 126000

Reorder the terms:
-3x + 2x2 = 126000

Solving
-3x + 2x2 = 126000

Solving for variable 'x'.

Reorder the terms:
-126000 + -3x + 2x2 = 126000 + -126000

Combine like terms: 126000 + -126000 = 0
-126000 + -3x + 2x2 = 0

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

Divide each side by '2'.
-63000 + -1.5x + x2 = 0

Move the constant term to the right:

Add '63000' to each side of the equation.
-63000 + -1.5x + 63000 + x2 = 0 + 63000

Reorder the terms:
-63000 + 63000 + -1.5x + x2 = 0 + 63000

Combine like terms: -63000 + 63000 = 0
0 + -1.5x + x2 = 0 + 63000
-1.5x + x2 = 0 + 63000

Combine like terms: 0 + 63000 = 63000
-1.5x + x2 = 63000

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 63000 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 63000 + 0.5625

Combine like terms: 63000 + 0.5625 = 63000.5625
0.5625 + -1.5x + x2 = 63000.5625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 63000.5625

Calculate the square root of the right side: 250.999128485

Break this problem into two subproblems by setting 
(x + -0.75) equal to 250.999128485 and -250.999128485.

Subproblem 1

x + -0.75 = 250.999128485 Simplifying x + -0.75 = 250.999128485 Reorder the terms: -0.75 + x = 250.999128485 Solving -0.75 + x = 250.999128485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 250.999128485 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 250.999128485 + 0.75 x = 250.999128485 + 0.75 Combine like terms: 250.999128485 + 0.75 = 251.749128485 x = 251.749128485 Simplifying x = 251.749128485

Subproblem 2

x + -0.75 = -250.999128485 Simplifying x + -0.75 = -250.999128485 Reorder the terms: -0.75 + x = -250.999128485 Solving -0.75 + x = -250.999128485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -250.999128485 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -250.999128485 + 0.75 x = -250.999128485 + 0.75 Combine like terms: -250.999128485 + 0.75 = -250.249128485 x = -250.249128485 Simplifying x = -250.249128485

Solution

The solution to the problem is based on the solutions from the subproblems. x = {251.749128485, -250.249128485}

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