x^2-60x=400

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Solution for x^2-60x=400 equation: 


Simplifying
x2 + -60x = 400

Reorder the terms:
-60x + x2 = 400

Solving
-60x + x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + -60x + x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + -60x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -60x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + -60x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -60x + x2 = 0 + 400
-60x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
-60x + x2 = 400

The x term is -60x.  Take half its coefficient (-30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
-60x + 900 + x2 = 400 + 900

Reorder the terms:
900 + -60x + x2 = 400 + 900

Combine like terms: 400 + 900 = 1300
900 + -60x + x2 = 1300

Factor a perfect square on the left side:
(x + -30)(x + -30) = 1300

Calculate the square root of the right side: 36.055512755

Break this problem into two subproblems by setting 
(x + -30) equal to 36.055512755 and -36.055512755.


Subproblem 1
x + -30 = 36.055512755

Simplifying
x + -30 = 36.055512755

Reorder the terms:
-30 + x = 36.055512755

Solving
-30 + x = 36.055512755

Solving for variable 'x'.

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

Add '30' to each side of the equation.
-30 + 30 + x = 36.055512755 + 30

Combine like terms: -30 + 30 = 0
0 + x = 36.055512755 + 30
x = 36.055512755 + 30

Combine like terms: 36.055512755 + 30 = 66.055512755
x = 66.055512755

Simplifying
x = 66.055512755


Subproblem 2
x + -30 = -36.055512755

Simplifying
x + -30 = -36.055512755

Reorder the terms:
-30 + x = -36.055512755

Solving
-30 + x = -36.055512755

Solving for variable 'x'.

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

Add '30' to each side of the equation.
-30 + 30 + x = -36.055512755 + 30

Combine like terms: -30 + 30 = 0
0 + x = -36.055512755 + 30
x = -36.055512755 + 30

Combine like terms: -36.055512755 + 30 = -6.055512755
x = -6.055512755

Simplifying
x = -6.055512755


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {66.055512755, -6.055512755}

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