a^2-30a-72=0

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Solution for a^2-30a-72=0 equation:


Simplifying
a2 + -30a + -72 = 0

Reorder the terms:
-72 + -30a + a2 = 0

Solving
-72 + -30a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + -30a + 72 + a2 = 0 + 72

Reorder the terms:
-72 + 72 + -30a + a2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + -30a + a2 = 0 + 72
-30a + a2 = 0 + 72

Combine like terms: 0 + 72 = 72
-30a + a2 = 72

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 = 72 + 225

Reorder the terms:
225 + -30a + a2 = 72 + 225

Combine like terms: 72 + 225 = 297
225 + -30a + a2 = 297

Factor a perfect square on the left side:
(a + -15)(a + -15) = 297

Calculate the square root of the right side: 17.23368794

Break this problem into two subproblems by setting 
(a + -15) equal to 17.23368794 and -17.23368794.

Subproblem 1

a + -15 = 17.23368794 Simplifying a + -15 = 17.23368794 Reorder the terms: -15 + a = 17.23368794 Solving -15 + a = 17.23368794 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 = 17.23368794 + 15 Combine like terms: -15 + 15 = 0 0 + a = 17.23368794 + 15 a = 17.23368794 + 15 Combine like terms: 17.23368794 + 15 = 32.23368794 a = 32.23368794 Simplifying a = 32.23368794

Subproblem 2

a + -15 = -17.23368794 Simplifying a + -15 = -17.23368794 Reorder the terms: -15 + a = -17.23368794 Solving -15 + a = -17.23368794 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 = -17.23368794 + 15 Combine like terms: -15 + 15 = 0 0 + a = -17.23368794 + 15 a = -17.23368794 + 15 Combine like terms: -17.23368794 + 15 = -2.23368794 a = -2.23368794 Simplifying a = -2.23368794

Solution

The solution to the problem is based on the solutions from the subproblems. a = {32.23368794, -2.23368794}

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