2x^2-24x+33=0

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Solution for 2x^2-24x+33=0 equation:


Simplifying
2x2 + -24x + 33 = 0

Reorder the terms:
33 + -24x + 2x2 = 0

Solving
33 + -24x + 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 + -12x + x2 = 0

Move the constant term to the right:

Add '-16.5' to each side of the equation.
16.5 + -12x + -16.5 + x2 = 0 + -16.5

Reorder the terms:
16.5 + -16.5 + -12x + x2 = 0 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + -12x + x2 = 0 + -16.5
-12x + x2 = 0 + -16.5

Combine like terms: 0 + -16.5 = -16.5
-12x + x2 = -16.5

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -16.5 + 36

Reorder the terms:
36 + -12x + x2 = -16.5 + 36

Combine like terms: -16.5 + 36 = 19.5
36 + -12x + x2 = 19.5

Factor a perfect square on the left side:
(x + -6)(x + -6) = 19.5

Calculate the square root of the right side: 4.415880433

Break this problem into two subproblems by setting 
(x + -6) equal to 4.415880433 and -4.415880433.

Subproblem 1

x + -6 = 4.415880433 Simplifying x + -6 = 4.415880433 Reorder the terms: -6 + x = 4.415880433 Solving -6 + x = 4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 4.415880433 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.415880433 + 6 x = 4.415880433 + 6 Combine like terms: 4.415880433 + 6 = 10.415880433 x = 10.415880433 Simplifying x = 10.415880433

Subproblem 2

x + -6 = -4.415880433 Simplifying x + -6 = -4.415880433 Reorder the terms: -6 + x = -4.415880433 Solving -6 + x = -4.415880433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -4.415880433 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.415880433 + 6 x = -4.415880433 + 6 Combine like terms: -4.415880433 + 6 = 1.584119567 x = 1.584119567 Simplifying x = 1.584119567

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.415880433, 1.584119567}

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