5x^2-26x+9=0

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Solution for 5x^2-26x+9=0 equation:


Simplifying
5x2 + -26x + 9 = 0

Reorder the terms:
9 + -26x + 5x2 = 0

Solving
9 + -26x + 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'.
1.8 + -5.2x + x2 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + -5.2x + -1.8 + x2 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + -5.2x + x2 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + -5.2x + x2 = 0 + -1.8
-5.2x + x2 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
-5.2x + x2 = -1.8

The x term is -5.2x.  Take half its coefficient (-2.6).
Square it (6.76) and add it to both sides.

Add '6.76' to each side of the equation.
-5.2x + 6.76 + x2 = -1.8 + 6.76

Reorder the terms:
6.76 + -5.2x + x2 = -1.8 + 6.76

Combine like terms: -1.8 + 6.76 = 4.96
6.76 + -5.2x + x2 = 4.96

Factor a perfect square on the left side:
(x + -2.6)(x + -2.6) = 4.96

Calculate the square root of the right side: 2.227105745

Break this problem into two subproblems by setting 
(x + -2.6) equal to 2.227105745 and -2.227105745.

Subproblem 1

x + -2.6 = 2.227105745 Simplifying x + -2.6 = 2.227105745 Reorder the terms: -2.6 + x = 2.227105745 Solving -2.6 + x = 2.227105745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 2.227105745 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 2.227105745 + 2.6 x = 2.227105745 + 2.6 Combine like terms: 2.227105745 + 2.6 = 4.827105745 x = 4.827105745 Simplifying x = 4.827105745

Subproblem 2

x + -2.6 = -2.227105745 Simplifying x + -2.6 = -2.227105745 Reorder the terms: -2.6 + x = -2.227105745 Solving -2.6 + x = -2.227105745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = -2.227105745 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -2.227105745 + 2.6 x = -2.227105745 + 2.6 Combine like terms: -2.227105745 + 2.6 = 0.372894255 x = 0.372894255 Simplifying x = 0.372894255

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.827105745, 0.372894255}

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