9x^2+640x-5500=0

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Solution for 9x^2+640x-5500=0 equation:


Simplifying
9x2 + 640x + -5500 = 0

Reorder the terms:
-5500 + 640x + 9x2 = 0

Solving
-5500 + 640x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-611.1111111 + 71.11111111x + x2 = 0

Move the constant term to the right:

Add '611.1111111' to each side of the equation.
-611.1111111 + 71.11111111x + 611.1111111 + x2 = 0 + 611.1111111

Reorder the terms:
-611.1111111 + 611.1111111 + 71.11111111x + x2 = 0 + 611.1111111

Combine like terms: -611.1111111 + 611.1111111 = 0.0000000
0.0000000 + 71.11111111x + x2 = 0 + 611.1111111
71.11111111x + x2 = 0 + 611.1111111

Combine like terms: 0 + 611.1111111 = 611.1111111
71.11111111x + x2 = 611.1111111

The x term is 71.11111111x.  Take half its coefficient (35.55555556).
Square it (1264.197531) and add it to both sides.

Add '1264.197531' to each side of the equation.
71.11111111x + 1264.197531 + x2 = 611.1111111 + 1264.197531

Reorder the terms:
1264.197531 + 71.11111111x + x2 = 611.1111111 + 1264.197531

Combine like terms: 611.1111111 + 1264.197531 = 1875.3086421
1264.197531 + 71.11111111x + x2 = 1875.3086421

Factor a perfect square on the left side:
(x + 35.55555556)(x + 35.55555556) = 1875.3086421

Calculate the square root of the right side: 43.304833935

Break this problem into two subproblems by setting 
(x + 35.55555556) equal to 43.304833935 and -43.304833935.

Subproblem 1

x + 35.55555556 = 43.304833935 Simplifying x + 35.55555556 = 43.304833935 Reorder the terms: 35.55555556 + x = 43.304833935 Solving 35.55555556 + x = 43.304833935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.55555556' to each side of the equation. 35.55555556 + -35.55555556 + x = 43.304833935 + -35.55555556 Combine like terms: 35.55555556 + -35.55555556 = 0.00000000 0.00000000 + x = 43.304833935 + -35.55555556 x = 43.304833935 + -35.55555556 Combine like terms: 43.304833935 + -35.55555556 = 7.749278375 x = 7.749278375 Simplifying x = 7.749278375

Subproblem 2

x + 35.55555556 = -43.304833935 Simplifying x + 35.55555556 = -43.304833935 Reorder the terms: 35.55555556 + x = -43.304833935 Solving 35.55555556 + x = -43.304833935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.55555556' to each side of the equation. 35.55555556 + -35.55555556 + x = -43.304833935 + -35.55555556 Combine like terms: 35.55555556 + -35.55555556 = 0.00000000 0.00000000 + x = -43.304833935 + -35.55555556 x = -43.304833935 + -35.55555556 Combine like terms: -43.304833935 + -35.55555556 = -78.860389495 x = -78.860389495 Simplifying x = -78.860389495

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.749278375, -78.860389495}

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