x^2-60x-45=0

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Solution for x^2-60x-45=0 equation: 


Simplifying
x2 + -60x + -45 = 0

Reorder the terms:
-45 + -60x + x2 = 0

Solving
-45 + -60x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -60x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + -60x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -60x + x2 = 0 + 45
-60x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
-60x + x2 = 45

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 = 45 + 900

Reorder the terms:
900 + -60x + x2 = 45 + 900

Combine like terms: 45 + 900 = 945
900 + -60x + x2 = 945

Factor a perfect square on the left side:
(x + -30)(x + -30) = 945

Calculate the square root of the right side: 30.740852298

Break this problem into two subproblems by setting 
(x + -30) equal to 30.740852298 and -30.740852298.


Subproblem 1
x + -30 = 30.740852298

Simplifying
x + -30 = 30.740852298

Reorder the terms:
-30 + x = 30.740852298

Solving
-30 + x = 30.740852298

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 = 30.740852298 + 30

Combine like terms: -30 + 30 = 0
0 + x = 30.740852298 + 30
x = 30.740852298 + 30

Combine like terms: 30.740852298 + 30 = 60.740852298
x = 60.740852298

Simplifying
x = 60.740852298


Subproblem 2
x + -30 = -30.740852298

Simplifying
x + -30 = -30.740852298

Reorder the terms:
-30 + x = -30.740852298

Solving
-30 + x = -30.740852298

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 = -30.740852298 + 30

Combine like terms: -30 + 30 = 0
0 + x = -30.740852298 + 30
x = -30.740852298 + 30

Combine like terms: -30.740852298 + 30 = -0.740852298
x = -0.740852298

Simplifying
x = -0.740852298


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {60.740852298, -0.740852298}

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