a^2-60a+180=0

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Solution for a^2-60a+180=0 equation:


Simplifying
a2 + -60a + 180 = 0

Reorder the terms:
180 + -60a + a2 = 0

Solving
180 + -60a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-180' to each side of the equation.
180 + -60a + -180 + a2 = 0 + -180

Reorder the terms:
180 + -180 + -60a + a2 = 0 + -180

Combine like terms: 180 + -180 = 0
0 + -60a + a2 = 0 + -180
-60a + a2 = 0 + -180

Combine like terms: 0 + -180 = -180
-60a + a2 = -180

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

Add '900' to each side of the equation.
-60a + 900 + a2 = -180 + 900

Reorder the terms:
900 + -60a + a2 = -180 + 900

Combine like terms: -180 + 900 = 720
900 + -60a + a2 = 720

Factor a perfect square on the left side:
(a + -30)(a + -30) = 720

Calculate the square root of the right side: 26.83281573

Break this problem into two subproblems by setting 
(a + -30) equal to 26.83281573 and -26.83281573.

Subproblem 1

a + -30 = 26.83281573 Simplifying a + -30 = 26.83281573 Reorder the terms: -30 + a = 26.83281573 Solving -30 + a = 26.83281573 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + a = 26.83281573 + 30 Combine like terms: -30 + 30 = 0 0 + a = 26.83281573 + 30 a = 26.83281573 + 30 Combine like terms: 26.83281573 + 30 = 56.83281573 a = 56.83281573 Simplifying a = 56.83281573

Subproblem 2

a + -30 = -26.83281573 Simplifying a + -30 = -26.83281573 Reorder the terms: -30 + a = -26.83281573 Solving -30 + a = -26.83281573 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + a = -26.83281573 + 30 Combine like terms: -30 + 30 = 0 0 + a = -26.83281573 + 30 a = -26.83281573 + 30 Combine like terms: -26.83281573 + 30 = 3.16718427 a = 3.16718427 Simplifying a = 3.16718427

Solution

The solution to the problem is based on the solutions from the subproblems. a = {56.83281573, 3.16718427}

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