x^2-72x+35=0

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Solution for x^2-72x+35=0 equation:


Simplifying
x2 + -72x + 35 = 0

Reorder the terms:
35 + -72x + x2 = 0

Solving
35 + -72x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + -72x + -35 + x2 = 0 + -35

Reorder the terms:
35 + -35 + -72x + x2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -72x + x2 = 0 + -35
-72x + x2 = 0 + -35

Combine like terms: 0 + -35 = -35
-72x + x2 = -35

The x term is -72x.  Take half its coefficient (-36).
Square it (1296) and add it to both sides.

Add '1296' to each side of the equation.
-72x + 1296 + x2 = -35 + 1296

Reorder the terms:
1296 + -72x + x2 = -35 + 1296

Combine like terms: -35 + 1296 = 1261
1296 + -72x + x2 = 1261

Factor a perfect square on the left side:
(x + -36)(x + -36) = 1261

Calculate the square root of the right side: 35.510561809

Break this problem into two subproblems by setting 
(x + -36) equal to 35.510561809 and -35.510561809.

Subproblem 1

x + -36 = 35.510561809 Simplifying x + -36 = 35.510561809 Reorder the terms: -36 + x = 35.510561809 Solving -36 + x = 35.510561809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = 35.510561809 + 36 Combine like terms: -36 + 36 = 0 0 + x = 35.510561809 + 36 x = 35.510561809 + 36 Combine like terms: 35.510561809 + 36 = 71.510561809 x = 71.510561809 Simplifying x = 71.510561809

Subproblem 2

x + -36 = -35.510561809 Simplifying x + -36 = -35.510561809 Reorder the terms: -36 + x = -35.510561809 Solving -36 + x = -35.510561809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = -35.510561809 + 36 Combine like terms: -36 + 36 = 0 0 + x = -35.510561809 + 36 x = -35.510561809 + 36 Combine like terms: -35.510561809 + 36 = 0.489438191 x = 0.489438191 Simplifying x = 0.489438191

Solution

The solution to the problem is based on the solutions from the subproblems. x = {71.510561809, 0.489438191}

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