.9x^2-90x-13000=0

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Solution for .9x^2-90x-13000=0 equation:


Simplifying
0.9x2 + -90x + -13000 = 0

Reorder the terms:
-13000 + -90x + 0.9x2 = 0

Solving
-13000 + -90x + 0.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.9'.
-14444.44444 + -100x + x2 = 0

Move the constant term to the right:

Add '14444.44444' to each side of the equation.
-14444.44444 + -100x + 14444.44444 + x2 = 0 + 14444.44444

Reorder the terms:
-14444.44444 + 14444.44444 + -100x + x2 = 0 + 14444.44444

Combine like terms: -14444.44444 + 14444.44444 = 0.00000
0.00000 + -100x + x2 = 0 + 14444.44444
-100x + x2 = 0 + 14444.44444

Combine like terms: 0 + 14444.44444 = 14444.44444
-100x + x2 = 14444.44444

The x term is -100x.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100x + 2500 + x2 = 14444.44444 + 2500

Reorder the terms:
2500 + -100x + x2 = 14444.44444 + 2500

Combine like terms: 14444.44444 + 2500 = 16944.44444
2500 + -100x + x2 = 16944.44444

Factor a perfect square on the left side:
(x + -50)(x + -50) = 16944.44444

Calculate the square root of the right side: 130.170827915

Break this problem into two subproblems by setting 
(x + -50) equal to 130.170827915 and -130.170827915.

Subproblem 1

x + -50 = 130.170827915 Simplifying x + -50 = 130.170827915 Reorder the terms: -50 + x = 130.170827915 Solving -50 + x = 130.170827915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 130.170827915 + 50 Combine like terms: -50 + 50 = 0 0 + x = 130.170827915 + 50 x = 130.170827915 + 50 Combine like terms: 130.170827915 + 50 = 180.170827915 x = 180.170827915 Simplifying x = 180.170827915

Subproblem 2

x + -50 = -130.170827915 Simplifying x + -50 = -130.170827915 Reorder the terms: -50 + x = -130.170827915 Solving -50 + x = -130.170827915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -130.170827915 + 50 Combine like terms: -50 + 50 = 0 0 + x = -130.170827915 + 50 x = -130.170827915 + 50 Combine like terms: -130.170827915 + 50 = -80.170827915 x = -80.170827915 Simplifying x = -80.170827915

Solution

The solution to the problem is based on the solutions from the subproblems. x = {180.170827915, -80.170827915}

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