4x^2-20x-19=0

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Solution for 4x^2-20x-19=0 equation:


Simplifying
4x2 + -20x + -19 = 0

Reorder the terms:
-19 + -20x + 4x2 = 0

Solving
-19 + -20x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-4.75 + -5x + x2 = 0

Move the constant term to the right:

Add '4.75' to each side of the equation.
-4.75 + -5x + 4.75 + x2 = 0 + 4.75

Reorder the terms:
-4.75 + 4.75 + -5x + x2 = 0 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + -5x + x2 = 0 + 4.75
-5x + x2 = 0 + 4.75

Combine like terms: 0 + 4.75 = 4.75
-5x + x2 = 4.75

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 4.75 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 4.75 + 6.25

Combine like terms: 4.75 + 6.25 = 11
6.25 + -5x + x2 = 11

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + -2.5 = 3.31662479 Simplifying x + -2.5 = 3.31662479 Reorder the terms: -2.5 + x = 3.31662479 Solving -2.5 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.31662479 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.31662479 + 2.5 x = 3.31662479 + 2.5 Combine like terms: 3.31662479 + 2.5 = 5.81662479 x = 5.81662479 Simplifying x = 5.81662479

Subproblem 2

x + -2.5 = -3.31662479 Simplifying x + -2.5 = -3.31662479 Reorder the terms: -2.5 + x = -3.31662479 Solving -2.5 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.31662479 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.31662479 + 2.5 x = -3.31662479 + 2.5 Combine like terms: -3.31662479 + 2.5 = -0.81662479 x = -0.81662479 Simplifying x = -0.81662479

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.81662479, -0.81662479}

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