a^2-3a-36=0

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Solution for a^2-3a-36=0 equation:


Simplifying
a2 + -3a + -36 = 0

Reorder the terms:
-36 + -3a + a2 = 0

Solving
-36 + -3a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -3a + 36 + a2 = 0 + 36

Reorder the terms:
-36 + 36 + -3a + a2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -3a + a2 = 0 + 36
-3a + a2 = 0 + 36

Combine like terms: 0 + 36 = 36
-3a + a2 = 36

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = 36 + 2.25

Reorder the terms:
2.25 + -3a + a2 = 36 + 2.25

Combine like terms: 36 + 2.25 = 38.25
2.25 + -3a + a2 = 38.25

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(a + -1.5) equal to 6.184658438 and -6.184658438.

Subproblem 1

a + -1.5 = 6.184658438 Simplifying a + -1.5 = 6.184658438 Reorder the terms: -1.5 + a = 6.184658438 Solving -1.5 + a = 6.184658438 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = 6.184658438 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 6.184658438 + 1.5 a = 6.184658438 + 1.5 Combine like terms: 6.184658438 + 1.5 = 7.684658438 a = 7.684658438 Simplifying a = 7.684658438

Subproblem 2

a + -1.5 = -6.184658438 Simplifying a + -1.5 = -6.184658438 Reorder the terms: -1.5 + a = -6.184658438 Solving -1.5 + a = -6.184658438 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = -6.184658438 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -6.184658438 + 1.5 a = -6.184658438 + 1.5 Combine like terms: -6.184658438 + 1.5 = -4.684658438 a = -4.684658438 Simplifying a = -4.684658438

Solution

The solution to the problem is based on the solutions from the subproblems. a = {7.684658438, -4.684658438}

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