5x^2-20x+6=0

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Solution for 5x^2-20x+6=0 equation:


Simplifying
5x2 + -20x + 6 = 0

Reorder the terms:
6 + -20x + 5x2 = 0

Solving
6 + -20x + 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'.
1.2 + -4x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -4x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -4x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -4x + x2 = 0 + -1.2
-4x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-4x + x2 = -1.2

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -1.2 + 4

Reorder the terms:
4 + -4x + x2 = -1.2 + 4

Combine like terms: -1.2 + 4 = 2.8
4 + -4x + x2 = 2.8

Factor a perfect square on the left side:
(x + -2)(x + -2) = 2.8

Calculate the square root of the right side: 1.673320053

Break this problem into two subproblems by setting 
(x + -2) equal to 1.673320053 and -1.673320053.

Subproblem 1

x + -2 = 1.673320053 Simplifying x + -2 = 1.673320053 Reorder the terms: -2 + x = 1.673320053 Solving -2 + x = 1.673320053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.673320053 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.673320053 + 2 x = 1.673320053 + 2 Combine like terms: 1.673320053 + 2 = 3.673320053 x = 3.673320053 Simplifying x = 3.673320053

Subproblem 2

x + -2 = -1.673320053 Simplifying x + -2 = -1.673320053 Reorder the terms: -2 + x = -1.673320053 Solving -2 + x = -1.673320053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.673320053 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.673320053 + 2 x = -1.673320053 + 2 Combine like terms: -1.673320053 + 2 = 0.326679947 x = 0.326679947 Simplifying x = 0.326679947

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.673320053, 0.326679947}

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