5x^2-25x+13=0

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Solution for 5x^2-25x+13=0 equation:


Simplifying
5x2 + -25x + 13 = 0

Reorder the terms:
13 + -25x + 5x2 = 0

Solving
13 + -25x + 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'.
2.6 + -5x + x2 = 0

Move the constant term to the right:

Add '-2.6' to each side of the equation.
2.6 + -5x + -2.6 + x2 = 0 + -2.6

Reorder the terms:
2.6 + -2.6 + -5x + x2 = 0 + -2.6

Combine like terms: 2.6 + -2.6 = 0.0
0.0 + -5x + x2 = 0 + -2.6
-5x + x2 = 0 + -2.6

Combine like terms: 0 + -2.6 = -2.6
-5x + x2 = -2.6

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -2.6 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -2.6 + 6.25

Combine like terms: -2.6 + 6.25 = 3.65
6.25 + -5x + x2 = 3.65

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 3.65

Calculate the square root of the right side: 1.910497317

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.910497317 and -1.910497317.

Subproblem 1

x + -2.5 = 1.910497317 Simplifying x + -2.5 = 1.910497317 Reorder the terms: -2.5 + x = 1.910497317 Solving -2.5 + x = 1.910497317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.910497317 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.910497317 + 2.5 x = 1.910497317 + 2.5 Combine like terms: 1.910497317 + 2.5 = 4.410497317 x = 4.410497317 Simplifying x = 4.410497317

Subproblem 2

x + -2.5 = -1.910497317 Simplifying x + -2.5 = -1.910497317 Reorder the terms: -2.5 + x = -1.910497317 Solving -2.5 + x = -1.910497317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.910497317 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.910497317 + 2.5 x = -1.910497317 + 2.5 Combine like terms: -1.910497317 + 2.5 = 0.589502683 x = 0.589502683 Simplifying x = 0.589502683

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.410497317, 0.589502683}

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