11x(19-1x)=196

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Solution for 11x(19-1x)=196 equation:


Simplifying
11x(19 + -1x) = 196
(19 * 11x + -1x * 11x) = 196
(209x + -11x2) = 196

Solving
209x + -11x2 = 196

Solving for variable 'x'.

Reorder the terms:
-196 + 209x + -11x2 = 196 + -196

Combine like terms: 196 + -196 = 0
-196 + 209x + -11x2 = 0

Begin completing the square.  Divide all terms by
-11 the coefficient of the squared term: 

Divide each side by '-11'.
17.81818182 + -19x + x2 = 0

Move the constant term to the right:

Add '-17.81818182' to each side of the equation.
17.81818182 + -19x + -17.81818182 + x2 = 0 + -17.81818182

Reorder the terms:
17.81818182 + -17.81818182 + -19x + x2 = 0 + -17.81818182

Combine like terms: 17.81818182 + -17.81818182 = 0.00000000
0.00000000 + -19x + x2 = 0 + -17.81818182
-19x + x2 = 0 + -17.81818182

Combine like terms: 0 + -17.81818182 = -17.81818182
-19x + x2 = -17.81818182

The x term is -19x.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19x + 90.25 + x2 = -17.81818182 + 90.25

Reorder the terms:
90.25 + -19x + x2 = -17.81818182 + 90.25

Combine like terms: -17.81818182 + 90.25 = 72.43181818
90.25 + -19x + x2 = 72.43181818

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 72.43181818

Calculate the square root of the right side: 8.510688467

Break this problem into two subproblems by setting 
(x + -9.5) equal to 8.510688467 and -8.510688467.

Subproblem 1

x + -9.5 = 8.510688467 Simplifying x + -9.5 = 8.510688467 Reorder the terms: -9.5 + x = 8.510688467 Solving -9.5 + x = 8.510688467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 8.510688467 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 8.510688467 + 9.5 x = 8.510688467 + 9.5 Combine like terms: 8.510688467 + 9.5 = 18.010688467 x = 18.010688467 Simplifying x = 18.010688467

Subproblem 2

x + -9.5 = -8.510688467 Simplifying x + -9.5 = -8.510688467 Reorder the terms: -9.5 + x = -8.510688467 Solving -9.5 + x = -8.510688467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -8.510688467 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -8.510688467 + 9.5 x = -8.510688467 + 9.5 Combine like terms: -8.510688467 + 9.5 = 0.989311533 x = 0.989311533 Simplifying x = 0.989311533

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.010688467, 0.989311533}

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