20x^2-19x-3=0

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Solution for 20x^2-19x-3=0 equation:


Simplifying
20x2 + -19x + -3 = 0

Reorder the terms:
-3 + -19x + 20x2 = 0

Solving
-3 + -19x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
-0.15 + -0.95x + x2 = 0

Move the constant term to the right:

Add '0.15' to each side of the equation.
-0.15 + -0.95x + 0.15 + x2 = 0 + 0.15

Reorder the terms:
-0.15 + 0.15 + -0.95x + x2 = 0 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + -0.95x + x2 = 0 + 0.15
-0.95x + x2 = 0 + 0.15

Combine like terms: 0 + 0.15 = 0.15
-0.95x + x2 = 0.15

The x term is -0.95x.  Take half its coefficient (-0.475).
Square it (0.225625) and add it to both sides.

Add '0.225625' to each side of the equation.
-0.95x + 0.225625 + x2 = 0.15 + 0.225625

Reorder the terms:
0.225625 + -0.95x + x2 = 0.15 + 0.225625

Combine like terms: 0.15 + 0.225625 = 0.375625
0.225625 + -0.95x + x2 = 0.375625

Factor a perfect square on the left side:
(x + -0.475)(x + -0.475) = 0.375625

Calculate the square root of the right side: 0.612882534

Break this problem into two subproblems by setting 
(x + -0.475) equal to 0.612882534 and -0.612882534.

Subproblem 1

x + -0.475 = 0.612882534 Simplifying x + -0.475 = 0.612882534 Reorder the terms: -0.475 + x = 0.612882534 Solving -0.475 + x = 0.612882534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.475' to each side of the equation. -0.475 + 0.475 + x = 0.612882534 + 0.475 Combine like terms: -0.475 + 0.475 = 0.000 0.000 + x = 0.612882534 + 0.475 x = 0.612882534 + 0.475 Combine like terms: 0.612882534 + 0.475 = 1.087882534 x = 1.087882534 Simplifying x = 1.087882534

Subproblem 2

x + -0.475 = -0.612882534 Simplifying x + -0.475 = -0.612882534 Reorder the terms: -0.475 + x = -0.612882534 Solving -0.475 + x = -0.612882534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.475' to each side of the equation. -0.475 + 0.475 + x = -0.612882534 + 0.475 Combine like terms: -0.475 + 0.475 = 0.000 0.000 + x = -0.612882534 + 0.475 x = -0.612882534 + 0.475 Combine like terms: -0.612882534 + 0.475 = -0.137882534 x = -0.137882534 Simplifying x = -0.137882534

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.087882534, -0.137882534}

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