11x^2+19x-20=0

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Solution for 11x^2+19x-20=0 equation:


Simplifying
11x2 + 19x + -20 = 0

Reorder the terms:
-20 + 19x + 11x2 = 0

Solving
-20 + 19x + 11x2 = 0

Solving for variable 'x'.

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

Divide each side by '11'.
-1.818181818 + 1.727272727x + x2 = 0

Move the constant term to the right:

Add '1.818181818' to each side of the equation.
-1.818181818 + 1.727272727x + 1.818181818 + x2 = 0 + 1.818181818

Reorder the terms:
-1.818181818 + 1.818181818 + 1.727272727x + x2 = 0 + 1.818181818

Combine like terms: -1.818181818 + 1.818181818 = 0.000000000
0.000000000 + 1.727272727x + x2 = 0 + 1.818181818
1.727272727x + x2 = 0 + 1.818181818

Combine like terms: 0 + 1.818181818 = 1.818181818
1.727272727x + x2 = 1.818181818

The x term is 1.727272727x.  Take half its coefficient (0.8636363635).
Square it (0.7458677684) and add it to both sides.

Add '0.7458677684' to each side of the equation.
1.727272727x + 0.7458677684 + x2 = 1.818181818 + 0.7458677684

Reorder the terms:
0.7458677684 + 1.727272727x + x2 = 1.818181818 + 0.7458677684

Combine like terms: 1.818181818 + 0.7458677684 = 2.5640495864
0.7458677684 + 1.727272727x + x2 = 2.5640495864

Factor a perfect square on the left side:
(x + 0.8636363635)(x + 0.8636363635) = 2.5640495864

Calculate the square root of the right side: 1.601264996

Break this problem into two subproblems by setting 
(x + 0.8636363635) equal to 1.601264996 and -1.601264996.

Subproblem 1

x + 0.8636363635 = 1.601264996 Simplifying x + 0.8636363635 = 1.601264996 Reorder the terms: 0.8636363635 + x = 1.601264996 Solving 0.8636363635 + x = 1.601264996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8636363635' to each side of the equation. 0.8636363635 + -0.8636363635 + x = 1.601264996 + -0.8636363635 Combine like terms: 0.8636363635 + -0.8636363635 = 0.0000000000 0.0000000000 + x = 1.601264996 + -0.8636363635 x = 1.601264996 + -0.8636363635 Combine like terms: 1.601264996 + -0.8636363635 = 0.7376286325 x = 0.7376286325 Simplifying x = 0.7376286325

Subproblem 2

x + 0.8636363635 = -1.601264996 Simplifying x + 0.8636363635 = -1.601264996 Reorder the terms: 0.8636363635 + x = -1.601264996 Solving 0.8636363635 + x = -1.601264996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8636363635' to each side of the equation. 0.8636363635 + -0.8636363635 + x = -1.601264996 + -0.8636363635 Combine like terms: 0.8636363635 + -0.8636363635 = 0.0000000000 0.0000000000 + x = -1.601264996 + -0.8636363635 x = -1.601264996 + -0.8636363635 Combine like terms: -1.601264996 + -0.8636363635 = -2.4649013595 x = -2.4649013595 Simplifying x = -2.4649013595

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7376286325, -2.4649013595}

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