5x^2-4x-11=0

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Solution for 5x^2-4x-11=0 equation:


Simplifying
5x2 + -4x + -11 = 0

Reorder the terms:
-11 + -4x + 5x2 = 0

Solving
-11 + -4x + 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 + -0.8x + x2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + -0.8x + 2.2 + x2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + -0.8x + x2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -0.8x + x2 = 0 + 2.2
-0.8x + x2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
-0.8x + x2 = 2.2

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 2.2 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 2.2 + 0.16

Combine like terms: 2.2 + 0.16 = 2.36
0.16 + -0.8x + x2 = 2.36

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 2.36

Calculate the square root of the right side: 1.53622915

Break this problem into two subproblems by setting 
(x + -0.4) equal to 1.53622915 and -1.53622915.

Subproblem 1

x + -0.4 = 1.53622915 Simplifying x + -0.4 = 1.53622915 Reorder the terms: -0.4 + x = 1.53622915 Solving -0.4 + x = 1.53622915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.53622915 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.53622915 + 0.4 x = 1.53622915 + 0.4 Combine like terms: 1.53622915 + 0.4 = 1.93622915 x = 1.93622915 Simplifying x = 1.93622915

Subproblem 2

x + -0.4 = -1.53622915 Simplifying x + -0.4 = -1.53622915 Reorder the terms: -0.4 + x = -1.53622915 Solving -0.4 + x = -1.53622915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.53622915 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.53622915 + 0.4 x = -1.53622915 + 0.4 Combine like terms: -1.53622915 + 0.4 = -1.13622915 x = -1.13622915 Simplifying x = -1.13622915

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.93622915, -1.13622915}

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