90x-9x^2-100=0

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Solution for 90x-9x^2-100=0 equation:


Simplifying
90x + -9x2 + -100 = 0

Reorder the terms:
-100 + 90x + -9x2 = 0

Solving
-100 + 90x + -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'.
11.11111111 + -10x + x2 = 0

Move the constant term to the right:

Add '-11.11111111' to each side of the equation.
11.11111111 + -10x + -11.11111111 + x2 = 0 + -11.11111111

Reorder the terms:
11.11111111 + -11.11111111 + -10x + x2 = 0 + -11.11111111

Combine like terms: 11.11111111 + -11.11111111 = 0.00000000
0.00000000 + -10x + x2 = 0 + -11.11111111
-10x + x2 = 0 + -11.11111111

Combine like terms: 0 + -11.11111111 = -11.11111111
-10x + x2 = -11.11111111

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -11.11111111 + 25

Reorder the terms:
25 + -10x + x2 = -11.11111111 + 25

Combine like terms: -11.11111111 + 25 = 13.88888889
25 + -10x + x2 = 13.88888889

Factor a perfect square on the left side:
(x + -5)(x + -5) = 13.88888889

Calculate the square root of the right side: 3.726779963

Break this problem into two subproblems by setting 
(x + -5) equal to 3.726779963 and -3.726779963.

Subproblem 1

x + -5 = 3.726779963 Simplifying x + -5 = 3.726779963 Reorder the terms: -5 + x = 3.726779963 Solving -5 + x = 3.726779963 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.726779963 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.726779963 + 5 x = 3.726779963 + 5 Combine like terms: 3.726779963 + 5 = 8.726779963 x = 8.726779963 Simplifying x = 8.726779963

Subproblem 2

x + -5 = -3.726779963 Simplifying x + -5 = -3.726779963 Reorder the terms: -5 + x = -3.726779963 Solving -5 + x = -3.726779963 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.726779963 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.726779963 + 5 x = -3.726779963 + 5 Combine like terms: -3.726779963 + 5 = 1.273220037 x = 1.273220037 Simplifying x = 1.273220037

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.726779963, 1.273220037}

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