25x^2-52x+26=0

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Solution for 25x^2-52x+26=0 equation:


Simplifying
25x2 + -52x + 26 = 0

Reorder the terms:
26 + -52x + 25x2 = 0

Solving
26 + -52x + 25x2 = 0

Solving for variable 'x'.

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

Divide each side by '25'.
1.04 + -2.08x + x2 = 0

Move the constant term to the right:

Add '-1.04' to each side of the equation.
1.04 + -2.08x + -1.04 + x2 = 0 + -1.04

Reorder the terms:
1.04 + -1.04 + -2.08x + x2 = 0 + -1.04

Combine like terms: 1.04 + -1.04 = 0.00
0.00 + -2.08x + x2 = 0 + -1.04
-2.08x + x2 = 0 + -1.04

Combine like terms: 0 + -1.04 = -1.04
-2.08x + x2 = -1.04

The x term is -2.08x.  Take half its coefficient (-1.04).
Square it (1.0816) and add it to both sides.

Add '1.0816' to each side of the equation.
-2.08x + 1.0816 + x2 = -1.04 + 1.0816

Reorder the terms:
1.0816 + -2.08x + x2 = -1.04 + 1.0816

Combine like terms: -1.04 + 1.0816 = 0.0416
1.0816 + -2.08x + x2 = 0.0416

Factor a perfect square on the left side:
(x + -1.04)(x + -1.04) = 0.0416

Calculate the square root of the right side: 0.203960781

Break this problem into two subproblems by setting 
(x + -1.04) equal to 0.203960781 and -0.203960781.

Subproblem 1

x + -1.04 = 0.203960781 Simplifying x + -1.04 = 0.203960781 Reorder the terms: -1.04 + x = 0.203960781 Solving -1.04 + x = 0.203960781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.04' to each side of the equation. -1.04 + 1.04 + x = 0.203960781 + 1.04 Combine like terms: -1.04 + 1.04 = 0.00 0.00 + x = 0.203960781 + 1.04 x = 0.203960781 + 1.04 Combine like terms: 0.203960781 + 1.04 = 1.243960781 x = 1.243960781 Simplifying x = 1.243960781

Subproblem 2

x + -1.04 = -0.203960781 Simplifying x + -1.04 = -0.203960781 Reorder the terms: -1.04 + x = -0.203960781 Solving -1.04 + x = -0.203960781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.04' to each side of the equation. -1.04 + 1.04 + x = -0.203960781 + 1.04 Combine like terms: -1.04 + 1.04 = 0.00 0.00 + x = -0.203960781 + 1.04 x = -0.203960781 + 1.04 Combine like terms: -0.203960781 + 1.04 = 0.836039219 x = 0.836039219 Simplifying x = 0.836039219

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.243960781, 0.836039219}

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