a^2-5a-12=0

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Solution for a^2-5a-12=0 equation:


Simplifying
a2 + -5a + -12 = 0

Reorder the terms:
-12 + -5a + a2 = 0

Solving
-12 + -5a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -5a + 12 + a2 = 0 + 12

Reorder the terms:
-12 + 12 + -5a + a2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -5a + a2 = 0 + 12
-5a + a2 = 0 + 12

Combine like terms: 0 + 12 = 12
-5a + a2 = 12

The a term is -5a.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5a + 6.25 + a2 = 12 + 6.25

Reorder the terms:
6.25 + -5a + a2 = 12 + 6.25

Combine like terms: 12 + 6.25 = 18.25
6.25 + -5a + a2 = 18.25

Factor a perfect square on the left side:
(a + -2.5)(a + -2.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(a + -2.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

a + -2.5 = 4.272001873 Simplifying a + -2.5 = 4.272001873 Reorder the terms: -2.5 + a = 4.272001873 Solving -2.5 + a = 4.272001873 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = 4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 4.272001873 + 2.5 a = 4.272001873 + 2.5 Combine like terms: 4.272001873 + 2.5 = 6.772001873 a = 6.772001873 Simplifying a = 6.772001873

Subproblem 2

a + -2.5 = -4.272001873 Simplifying a + -2.5 = -4.272001873 Reorder the terms: -2.5 + a = -4.272001873 Solving -2.5 + a = -4.272001873 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = -4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -4.272001873 + 2.5 a = -4.272001873 + 2.5 Combine like terms: -4.272001873 + 2.5 = -1.772001873 a = -1.772001873 Simplifying a = -1.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. a = {6.772001873, -1.772001873}

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