x^2-70x+89=0

Solution for x^2-70x+89=0 equation:

Simplifying
x2 + -70x + 89 = 0

Reorder the terms:
89 + -70x + x2 = 0

Solving
89 + -70x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-89' to each side of the equation.
89 + -70x + -89 + x2 = 0 + -89

Reorder the terms:
89 + -89 + -70x + x2 = 0 + -89

Combine like terms: 89 + -89 = 0
0 + -70x + x2 = 0 + -89
-70x + x2 = 0 + -89

Combine like terms: 0 + -89 = -89
-70x + x2 = -89

The x term is -70x.  Take half its coefficient (-35).
Square it (1225) and add it to both sides.

Add '1225' to each side of the equation.
-70x + 1225 + x2 = -89 + 1225

Reorder the terms:
1225 + -70x + x2 = -89 + 1225

Combine like terms: -89 + 1225 = 1136
1225 + -70x + x2 = 1136

Factor a perfect square on the left side:
(x + -35)(x + -35) = 1136

Calculate the square root of the right side: 33.704599093

Break this problem into two subproblems by setting 
(x + -35) equal to 33.704599093 and -33.704599093.

Subproblem 1
x + -35 = 33.704599093

Simplifying
x + -35 = 33.704599093

Reorder the terms:
-35 + x = 33.704599093

Solving
-35 + x = 33.704599093

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '35' to each side of the equation.
-35 + 35 + x = 33.704599093 + 35

Combine like terms: -35 + 35 = 0
0 + x = 33.704599093 + 35
x = 33.704599093 + 35

Combine like terms: 33.704599093 + 35 = 68.704599093
x = 68.704599093

Simplifying
x = 68.704599093

Subproblem 2
x + -35 = -33.704599093

Simplifying
x + -35 = -33.704599093

Reorder the terms:
-35 + x = -33.704599093

Solving
-35 + x = -33.704599093

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '35' to each side of the equation.
-35 + 35 + x = -33.704599093 + 35

Combine like terms: -35 + 35 = 0
0 + x = -33.704599093 + 35
x = -33.704599093 + 35

Combine like terms: -33.704599093 + 35 = 1.295400907
x = 1.295400907

Simplifying
x = 1.295400907

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {68.704599093, 1.295400907}