4x^2-20x+11=0

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Solution for 4x^2-20x+11=0 equation:


Simplifying
4x2 + -20x + 11 = 0

Reorder the terms:
11 + -20x + 4x2 = 0

Solving
11 + -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'.
2.75 + -5x + x2 = 0

Move the constant term to the right:

Add '-2.75' to each side of the equation.
2.75 + -5x + -2.75 + x2 = 0 + -2.75

Reorder the terms:
2.75 + -2.75 + -5x + x2 = 0 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + -5x + x2 = 0 + -2.75
-5x + x2 = 0 + -2.75

Combine like terms: 0 + -2.75 = -2.75
-5x + x2 = -2.75

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 = -2.75 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -2.75 + 6.25

Combine like terms: -2.75 + 6.25 = 3.5
6.25 + -5x + x2 = 3.5

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.870828693 and -1.870828693.

Subproblem 1

x + -2.5 = 1.870828693 Simplifying x + -2.5 = 1.870828693 Reorder the terms: -2.5 + x = 1.870828693 Solving -2.5 + x = 1.870828693 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 = 1.870828693 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.870828693 + 2.5 x = 1.870828693 + 2.5 Combine like terms: 1.870828693 + 2.5 = 4.370828693 x = 4.370828693 Simplifying x = 4.370828693

Subproblem 2

x + -2.5 = -1.870828693 Simplifying x + -2.5 = -1.870828693 Reorder the terms: -2.5 + x = -1.870828693 Solving -2.5 + x = -1.870828693 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 = -1.870828693 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.870828693 + 2.5 x = -1.870828693 + 2.5 Combine like terms: -1.870828693 + 2.5 = 0.629171307 x = 0.629171307 Simplifying x = 0.629171307

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.370828693, 0.629171307}

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