0=x^2-52x+64

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Solution for 0=x^2-52x+64 equation:


Simplifying
0 = x2 + -52x + 64

Reorder the terms:
0 = 64 + -52x + x2

Solving
0 = 64 + -52x + x2

Solving for variable 'x'.

Combine like terms: 0 + -64 = -64
-64 + 52x + -1x2 = 64 + -52x + x2 + -64 + 52x + -1x2

Reorder the terms:
-64 + 52x + -1x2 = 64 + -64 + -52x + 52x + x2 + -1x2

Combine like terms: 64 + -64 = 0
-64 + 52x + -1x2 = 0 + -52x + 52x + x2 + -1x2
-64 + 52x + -1x2 = -52x + 52x + x2 + -1x2

Combine like terms: -52x + 52x = 0
-64 + 52x + -1x2 = 0 + x2 + -1x2
-64 + 52x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-64 + 52x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
64 + -52x + x2 = 0

Move the constant term to the right:

Add '-64' to each side of the equation.
64 + -52x + -64 + x2 = 0 + -64

Reorder the terms:
64 + -64 + -52x + x2 = 0 + -64

Combine like terms: 64 + -64 = 0
0 + -52x + x2 = 0 + -64
-52x + x2 = 0 + -64

Combine like terms: 0 + -64 = -64
-52x + x2 = -64

The x term is -52x.  Take half its coefficient (-26).
Square it (676) and add it to both sides.

Add '676' to each side of the equation.
-52x + 676 + x2 = -64 + 676

Reorder the terms:
676 + -52x + x2 = -64 + 676

Combine like terms: -64 + 676 = 612
676 + -52x + x2 = 612

Factor a perfect square on the left side:
(x + -26)(x + -26) = 612

Calculate the square root of the right side: 24.738633754

Break this problem into two subproblems by setting 
(x + -26) equal to 24.738633754 and -24.738633754.

Subproblem 1

x + -26 = 24.738633754 Simplifying x + -26 = 24.738633754 Reorder the terms: -26 + x = 24.738633754 Solving -26 + x = 24.738633754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = 24.738633754 + 26 Combine like terms: -26 + 26 = 0 0 + x = 24.738633754 + 26 x = 24.738633754 + 26 Combine like terms: 24.738633754 + 26 = 50.738633754 x = 50.738633754 Simplifying x = 50.738633754

Subproblem 2

x + -26 = -24.738633754 Simplifying x + -26 = -24.738633754 Reorder the terms: -26 + x = -24.738633754 Solving -26 + x = -24.738633754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = -24.738633754 + 26 Combine like terms: -26 + 26 = 0 0 + x = -24.738633754 + 26 x = -24.738633754 + 26 Combine like terms: -24.738633754 + 26 = 1.261366246 x = 1.261366246 Simplifying x = 1.261366246

Solution

The solution to the problem is based on the solutions from the subproblems. x = {50.738633754, 1.261366246}

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