70x-x^2+105=0

Solution for 70x-x^2+105=0 equation:

Simplifying
70x + -1x2 + 105 = 0

Reorder the terms:
105 + 70x + -1x2 = 0

Solving
105 + 70x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
-105 + -70x + x2 = 0

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + -70x + 105 + x2 = 0 + 105

Reorder the terms:
-105 + 105 + -70x + x2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + -70x + x2 = 0 + 105
-70x + x2 = 0 + 105

Combine like terms: 0 + 105 = 105
-70x + x2 = 105

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 = 105 + 1225

Reorder the terms:
1225 + -70x + x2 = 105 + 1225

Combine like terms: 105 + 1225 = 1330
1225 + -70x + x2 = 1330

Factor a perfect square on the left side:
(x + -35)(x + -35) = 1330

Calculate the square root of the right side: 36.469165058

Break this problem into two subproblems by setting 
(x + -35) equal to 36.469165058 and -36.469165058.

Subproblem 1
x + -35 = 36.469165058

Simplifying
x + -35 = 36.469165058

Reorder the terms:
-35 + x = 36.469165058

Solving
-35 + x = 36.469165058

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 = 36.469165058 + 35

Combine like terms: -35 + 35 = 0
0 + x = 36.469165058 + 35
x = 36.469165058 + 35

Combine like terms: 36.469165058 + 35 = 71.469165058
x = 71.469165058

Simplifying
x = 71.469165058

Subproblem 2
x + -35 = -36.469165058

Simplifying
x + -35 = -36.469165058

Reorder the terms:
-35 + x = -36.469165058

Solving
-35 + x = -36.469165058

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 = -36.469165058 + 35

Combine like terms: -35 + 35 = 0
0 + x = -36.469165058 + 35
x = -36.469165058 + 35

Combine like terms: -36.469165058 + 35 = -1.469165058
x = -1.469165058

Simplifying
x = -1.469165058

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {71.469165058, -1.469165058}