5X^2-66X+1=0

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Solution for 5X^2-66X+1=0 equation:


Simplifying
5X2 + -66X + 1 = 0

Reorder the terms:
1 + -66X + 5X2 = 0

Solving
1 + -66X + 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'.
0.2 + -13.2X + X2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -13.2X + -0.2 + X2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -13.2X + X2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -13.2X + X2 = 0 + -0.2
-13.2X + X2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-13.2X + X2 = -0.2

The X term is -13.2X.  Take half its coefficient (-6.6).
Square it (43.56) and add it to both sides.

Add '43.56' to each side of the equation.
-13.2X + 43.56 + X2 = -0.2 + 43.56

Reorder the terms:
43.56 + -13.2X + X2 = -0.2 + 43.56

Combine like terms: -0.2 + 43.56 = 43.36
43.56 + -13.2X + X2 = 43.36

Factor a perfect square on the left side:
(X + -6.6)(X + -6.6) = 43.36

Calculate the square root of the right side: 6.584831053

Break this problem into two subproblems by setting 
(X + -6.6) equal to 6.584831053 and -6.584831053.

Subproblem 1

X + -6.6 = 6.584831053 Simplifying X + -6.6 = 6.584831053 Reorder the terms: -6.6 + X = 6.584831053 Solving -6.6 + X = 6.584831053 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6.6' to each side of the equation. -6.6 + 6.6 + X = 6.584831053 + 6.6 Combine like terms: -6.6 + 6.6 = 0.0 0.0 + X = 6.584831053 + 6.6 X = 6.584831053 + 6.6 Combine like terms: 6.584831053 + 6.6 = 13.184831053 X = 13.184831053 Simplifying X = 13.184831053

Subproblem 2

X + -6.6 = -6.584831053 Simplifying X + -6.6 = -6.584831053 Reorder the terms: -6.6 + X = -6.584831053 Solving -6.6 + X = -6.584831053 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6.6' to each side of the equation. -6.6 + 6.6 + X = -6.584831053 + 6.6 Combine like terms: -6.6 + 6.6 = 0.0 0.0 + X = -6.584831053 + 6.6 X = -6.584831053 + 6.6 Combine like terms: -6.584831053 + 6.6 = 0.015168947 X = 0.015168947 Simplifying X = 0.015168947

Solution

The solution to the problem is based on the solutions from the subproblems. X = {13.184831053, 0.015168947}

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