2x^2-26x+69=0

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Solution for 2x^2-26x+69=0 equation:


Simplifying
2x2 + -26x + 69 = 0

Reorder the terms:
69 + -26x + 2x2 = 0

Solving
69 + -26x + 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'.
34.5 + -13x + x2 = 0

Move the constant term to the right:

Add '-34.5' to each side of the equation.
34.5 + -13x + -34.5 + x2 = 0 + -34.5

Reorder the terms:
34.5 + -34.5 + -13x + x2 = 0 + -34.5

Combine like terms: 34.5 + -34.5 = 0.0
0.0 + -13x + x2 = 0 + -34.5
-13x + x2 = 0 + -34.5

Combine like terms: 0 + -34.5 = -34.5
-13x + x2 = -34.5

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -34.5 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -34.5 + 42.25

Combine like terms: -34.5 + 42.25 = 7.75
42.25 + -13x + x2 = 7.75

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 7.75

Calculate the square root of the right side: 2.783882181

Break this problem into two subproblems by setting 
(x + -6.5) equal to 2.783882181 and -2.783882181.

Subproblem 1

x + -6.5 = 2.783882181 Simplifying x + -6.5 = 2.783882181 Reorder the terms: -6.5 + x = 2.783882181 Solving -6.5 + x = 2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 2.783882181 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 2.783882181 + 6.5 x = 2.783882181 + 6.5 Combine like terms: 2.783882181 + 6.5 = 9.283882181 x = 9.283882181 Simplifying x = 9.283882181

Subproblem 2

x + -6.5 = -2.783882181 Simplifying x + -6.5 = -2.783882181 Reorder the terms: -6.5 + x = -2.783882181 Solving -6.5 + x = -2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -2.783882181 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -2.783882181 + 6.5 x = -2.783882181 + 6.5 Combine like terms: -2.783882181 + 6.5 = 3.716117819 x = 3.716117819 Simplifying x = 3.716117819

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.283882181, 3.716117819}

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