x^2-63x+60=0

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Solution for x^2-63x+60=0 equation:


Simplifying
x2 + -63x + 60 = 0

Reorder the terms:
60 + -63x + x2 = 0

Solving
60 + -63x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + -63x + -60 + x2 = 0 + -60

Reorder the terms:
60 + -60 + -63x + x2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -63x + x2 = 0 + -60
-63x + x2 = 0 + -60

Combine like terms: 0 + -60 = -60
-63x + x2 = -60

The x term is -63x.  Take half its coefficient (-31.5).
Square it (992.25) and add it to both sides.

Add '992.25' to each side of the equation.
-63x + 992.25 + x2 = -60 + 992.25

Reorder the terms:
992.25 + -63x + x2 = -60 + 992.25

Combine like terms: -60 + 992.25 = 932.25
992.25 + -63x + x2 = 932.25

Factor a perfect square on the left side:
(x + -31.5)(x + -31.5) = 932.25

Calculate the square root of the right side: 30.532769282

Break this problem into two subproblems by setting 
(x + -31.5) equal to 30.532769282 and -30.532769282.

Subproblem 1

x + -31.5 = 30.532769282 Simplifying x + -31.5 = 30.532769282 Reorder the terms: -31.5 + x = 30.532769282 Solving -31.5 + x = 30.532769282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.5' to each side of the equation. -31.5 + 31.5 + x = 30.532769282 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + x = 30.532769282 + 31.5 x = 30.532769282 + 31.5 Combine like terms: 30.532769282 + 31.5 = 62.032769282 x = 62.032769282 Simplifying x = 62.032769282

Subproblem 2

x + -31.5 = -30.532769282 Simplifying x + -31.5 = -30.532769282 Reorder the terms: -31.5 + x = -30.532769282 Solving -31.5 + x = -30.532769282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.5' to each side of the equation. -31.5 + 31.5 + x = -30.532769282 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + x = -30.532769282 + 31.5 x = -30.532769282 + 31.5 Combine like terms: -30.532769282 + 31.5 = 0.967230718 x = 0.967230718 Simplifying x = 0.967230718

Solution

The solution to the problem is based on the solutions from the subproblems. x = {62.032769282, 0.967230718}

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