4x^2-26x+13=0

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Solution for 4x^2-26x+13=0 equation:


Simplifying
4x2 + -26x + 13 = 0

Reorder the terms:
13 + -26x + 4x2 = 0

Solving
13 + -26x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
3.25 + -6.5x + x2 = 0

Move the constant term to the right:

Add '-3.25' to each side of the equation.
3.25 + -6.5x + -3.25 + x2 = 0 + -3.25

Reorder the terms:
3.25 + -3.25 + -6.5x + x2 = 0 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + -6.5x + x2 = 0 + -3.25
-6.5x + x2 = 0 + -3.25

Combine like terms: 0 + -3.25 = -3.25
-6.5x + x2 = -3.25

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = -3.25 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = -3.25 + 10.5625

Combine like terms: -3.25 + 10.5625 = 7.3125
10.5625 + -6.5x + x2 = 7.3125

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 7.3125

Calculate the square root of the right side: 2.704163457

Break this problem into two subproblems by setting 
(x + -3.25) equal to 2.704163457 and -2.704163457.

Subproblem 1

x + -3.25 = 2.704163457 Simplifying x + -3.25 = 2.704163457 Reorder the terms: -3.25 + x = 2.704163457 Solving -3.25 + x = 2.704163457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 2.704163457 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 2.704163457 + 3.25 x = 2.704163457 + 3.25 Combine like terms: 2.704163457 + 3.25 = 5.954163457 x = 5.954163457 Simplifying x = 5.954163457

Subproblem 2

x + -3.25 = -2.704163457 Simplifying x + -3.25 = -2.704163457 Reorder the terms: -3.25 + x = -2.704163457 Solving -3.25 + x = -2.704163457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -2.704163457 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -2.704163457 + 3.25 x = -2.704163457 + 3.25 Combine like terms: -2.704163457 + 3.25 = 0.545836543 x = 0.545836543 Simplifying x = 0.545836543

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.954163457, 0.545836543}

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