5x^2-5x-11=0

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Solution for 5x^2-5x-11=0 equation:


Simplifying
5x2 + -5x + -11 = 0

Reorder the terms:
-11 + -5x + 5x2 = 0

Solving
-11 + -5x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-2.2 + -1x + x2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + -1x + 2.2 + x2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + -1x + x2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -1x + x2 = 0 + 2.2
-1x + x2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
-1x + x2 = 2.2

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 2.2 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 2.2 + 0.25

Combine like terms: 2.2 + 0.25 = 2.45
0.25 + -1x + x2 = 2.45

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 2.45

Calculate the square root of the right side: 1.565247584

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.565247584 and -1.565247584.

Subproblem 1

x + -0.5 = 1.565247584 Simplifying x + -0.5 = 1.565247584 Reorder the terms: -0.5 + x = 1.565247584 Solving -0.5 + x = 1.565247584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.565247584 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.565247584 + 0.5 x = 1.565247584 + 0.5 Combine like terms: 1.565247584 + 0.5 = 2.065247584 x = 2.065247584 Simplifying x = 2.065247584

Subproblem 2

x + -0.5 = -1.565247584 Simplifying x + -0.5 = -1.565247584 Reorder the terms: -0.5 + x = -1.565247584 Solving -0.5 + x = -1.565247584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.565247584 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.565247584 + 0.5 x = -1.565247584 + 0.5 Combine like terms: -1.565247584 + 0.5 = -1.065247584 x = -1.065247584 Simplifying x = -1.065247584

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.065247584, -1.065247584}

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