22X^2+21X-19=0

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Solution for 22X^2+21X-19=0 equation:


Simplifying
22X2 + 21X + -19 = 0

Reorder the terms:
-19 + 21X + 22X2 = 0

Solving
-19 + 21X + 22X2 = 0

Solving for variable 'X'.

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

Divide each side by '22'.
-0.8636363636 + 0.9545454545X + X2 = 0

Move the constant term to the right:

Add '0.8636363636' to each side of the equation.
-0.8636363636 + 0.9545454545X + 0.8636363636 + X2 = 0 + 0.8636363636

Reorder the terms:
-0.8636363636 + 0.8636363636 + 0.9545454545X + X2 = 0 + 0.8636363636

Combine like terms: -0.8636363636 + 0.8636363636 = 0.0000000000
0.0000000000 + 0.9545454545X + X2 = 0 + 0.8636363636
0.9545454545X + X2 = 0 + 0.8636363636

Combine like terms: 0 + 0.8636363636 = 0.8636363636
0.9545454545X + X2 = 0.8636363636

The X term is 0.9545454545X.  Take half its coefficient (0.4772727273).
Square it (0.2277892562) and add it to both sides.

Add '0.2277892562' to each side of the equation.
0.9545454545X + 0.2277892562 + X2 = 0.8636363636 + 0.2277892562

Reorder the terms:
0.2277892562 + 0.9545454545X + X2 = 0.8636363636 + 0.2277892562

Combine like terms: 0.8636363636 + 0.2277892562 = 1.0914256198
0.2277892562 + 0.9545454545X + X2 = 1.0914256198

Factor a perfect square on the left side:
(X + 0.4772727273)(X + 0.4772727273) = 1.0914256198

Calculate the square root of the right side: 1.044713176

Break this problem into two subproblems by setting 
(X + 0.4772727273) equal to 1.044713176 and -1.044713176.

Subproblem 1

X + 0.4772727273 = 1.044713176 Simplifying X + 0.4772727273 = 1.044713176 Reorder the terms: 0.4772727273 + X = 1.044713176 Solving 0.4772727273 + X = 1.044713176 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.4772727273' to each side of the equation. 0.4772727273 + -0.4772727273 + X = 1.044713176 + -0.4772727273 Combine like terms: 0.4772727273 + -0.4772727273 = 0.0000000000 0.0000000000 + X = 1.044713176 + -0.4772727273 X = 1.044713176 + -0.4772727273 Combine like terms: 1.044713176 + -0.4772727273 = 0.5674404487 X = 0.5674404487 Simplifying X = 0.5674404487

Subproblem 2

X + 0.4772727273 = -1.044713176 Simplifying X + 0.4772727273 = -1.044713176 Reorder the terms: 0.4772727273 + X = -1.044713176 Solving 0.4772727273 + X = -1.044713176 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.4772727273' to each side of the equation. 0.4772727273 + -0.4772727273 + X = -1.044713176 + -0.4772727273 Combine like terms: 0.4772727273 + -0.4772727273 = 0.0000000000 0.0000000000 + X = -1.044713176 + -0.4772727273 X = -1.044713176 + -0.4772727273 Combine like terms: -1.044713176 + -0.4772727273 = -1.5219859033 X = -1.5219859033 Simplifying X = -1.5219859033

Solution

The solution to the problem is based on the solutions from the subproblems. X = {0.5674404487, -1.5219859033}

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