2x^2-20x-3=0

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


Simplifying
2x2 + -20x + -3 = 0

Reorder the terms:
-3 + -20x + 2x2 = 0

Solving
-3 + -20x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-1.5 + -10x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -10x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -10x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -10x + x2 = 0 + 1.5
-10x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-10x + x2 = 1.5

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 1.5 + 25

Reorder the terms:
25 + -10x + x2 = 1.5 + 25

Combine like terms: 1.5 + 25 = 26.5
25 + -10x + x2 = 26.5

Factor a perfect square on the left side:
(x + -5)(x + -5) = 26.5

Calculate the square root of the right side: 5.14781507

Break this problem into two subproblems by setting 
(x + -5) equal to 5.14781507 and -5.14781507.

Subproblem 1

x + -5 = 5.14781507 Simplifying x + -5 = 5.14781507 Reorder the terms: -5 + x = 5.14781507 Solving -5 + x = 5.14781507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.14781507 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.14781507 + 5 x = 5.14781507 + 5 Combine like terms: 5.14781507 + 5 = 10.14781507 x = 10.14781507 Simplifying x = 10.14781507

Subproblem 2

x + -5 = -5.14781507 Simplifying x + -5 = -5.14781507 Reorder the terms: -5 + x = -5.14781507 Solving -5 + x = -5.14781507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.14781507 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.14781507 + 5 x = -5.14781507 + 5 Combine like terms: -5.14781507 + 5 = -0.14781507 x = -0.14781507 Simplifying x = -0.14781507

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.14781507, -0.14781507}

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