a^2-30a-180=

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Solution for a^2-30a-180= equation:


Simplifying
a2 + -30a + -180 = 0

Reorder the terms:
-180 + -30a + a2 = 0

Solving
-180 + -30a + 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 + -30a + 180 + a2 = 0 + 180

Reorder the terms:
-180 + 180 + -30a + a2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + -30a + a2 = 0 + 180
-30a + a2 = 0 + 180

Combine like terms: 0 + 180 = 180
-30a + a2 = 180

The a term is -30a.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30a + 225 + a2 = 180 + 225

Reorder the terms:
225 + -30a + a2 = 180 + 225

Combine like terms: 180 + 225 = 405
225 + -30a + a2 = 405

Factor a perfect square on the left side:
(a + -15)(a + -15) = 405

Calculate the square root of the right side: 20.124611797

Break this problem into two subproblems by setting 
(a + -15) equal to 20.124611797 and -20.124611797.

Subproblem 1

a + -15 = 20.124611797 Simplifying a + -15 = 20.124611797 Reorder the terms: -15 + a = 20.124611797 Solving -15 + a = 20.124611797 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + a = 20.124611797 + 15 Combine like terms: -15 + 15 = 0 0 + a = 20.124611797 + 15 a = 20.124611797 + 15 Combine like terms: 20.124611797 + 15 = 35.124611797 a = 35.124611797 Simplifying a = 35.124611797

Subproblem 2

a + -15 = -20.124611797 Simplifying a + -15 = -20.124611797 Reorder the terms: -15 + a = -20.124611797 Solving -15 + a = -20.124611797 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + a = -20.124611797 + 15 Combine like terms: -15 + 15 = 0 0 + a = -20.124611797 + 15 a = -20.124611797 + 15 Combine like terms: -20.124611797 + 15 = -5.124611797 a = -5.124611797 Simplifying a = -5.124611797

Solution

The solution to the problem is based on the solutions from the subproblems. a = {35.124611797, -5.124611797}

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