2x^2-20x+33=0

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Solution for 2x^2-20x+33=0 equation:


Simplifying
2x2 + -20x + 33 = 0

Reorder the terms:
33 + -20x + 2x2 = 0

Solving
33 + -20x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
16.5 + -10x + x2 = 0

Move the constant term to the right:

Add '-16.5' to each side of the equation.
16.5 + -10x + -16.5 + x2 = 0 + -16.5

Reorder the terms:
16.5 + -16.5 + -10x + x2 = 0 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + -10x + x2 = 0 + -16.5
-10x + x2 = 0 + -16.5

Combine like terms: 0 + -16.5 = -16.5
-10x + x2 = -16.5

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -16.5 + 25

Reorder the terms:
25 + -10x + x2 = -16.5 + 25

Combine like terms: -16.5 + 25 = 8.5
25 + -10x + x2 = 8.5

Factor a perfect square on the left side:
(x + -5)(x + -5) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(x + -5) equal to 2.915475947 and -2.915475947.

Subproblem 1

x + -5 = 2.915475947 Simplifying x + -5 = 2.915475947 Reorder the terms: -5 + x = 2.915475947 Solving -5 + x = 2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 2.915475947 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.915475947 + 5 x = 2.915475947 + 5 Combine like terms: 2.915475947 + 5 = 7.915475947 x = 7.915475947 Simplifying x = 7.915475947

Subproblem 2

x + -5 = -2.915475947 Simplifying x + -5 = -2.915475947 Reorder the terms: -5 + x = -2.915475947 Solving -5 + x = -2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -2.915475947 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.915475947 + 5 x = -2.915475947 + 5 Combine like terms: -2.915475947 + 5 = 2.084524053 x = 2.084524053 Simplifying x = 2.084524053

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.915475947, 2.084524053}

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