2x^2-10x-11=0

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Solution for 2x^2-10x-11=0 equation:


Simplifying
2x2 + -10x + -11 = 0

Reorder the terms:
-11 + -10x + 2x2 = 0

Solving
-11 + -10x + 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'.
-5.5 + -5x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -5x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -5x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -5x + x2 = 0 + 5.5
-5x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-5x + x2 = 5.5

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 = 5.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 5.5 + 6.25

Combine like terms: 5.5 + 6.25 = 11.75
6.25 + -5x + x2 = 11.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 11.75

Calculate the square root of the right side: 3.4278273

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.4278273 and -3.4278273.

Subproblem 1

x + -2.5 = 3.4278273 Simplifying x + -2.5 = 3.4278273 Reorder the terms: -2.5 + x = 3.4278273 Solving -2.5 + x = 3.4278273 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 = 3.4278273 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.4278273 + 2.5 x = 3.4278273 + 2.5 Combine like terms: 3.4278273 + 2.5 = 5.9278273 x = 5.9278273 Simplifying x = 5.9278273

Subproblem 2

x + -2.5 = -3.4278273 Simplifying x + -2.5 = -3.4278273 Reorder the terms: -2.5 + x = -3.4278273 Solving -2.5 + x = -3.4278273 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 = -3.4278273 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.4278273 + 2.5 x = -3.4278273 + 2.5 Combine like terms: -3.4278273 + 2.5 = -0.9278273 x = -0.9278273 Simplifying x = -0.9278273

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.9278273, -0.9278273}

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