a^2-3a-20=0

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Solution for a^2-3a-20=0 equation:


Simplifying
a2 + -3a + -20 = 0

Reorder the terms:
-20 + -3a + a2 = 0

Solving
-20 + -3a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -3a + 20 + a2 = 0 + 20

Reorder the terms:
-20 + 20 + -3a + a2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -3a + a2 = 0 + 20
-3a + a2 = 0 + 20

Combine like terms: 0 + 20 = 20
-3a + a2 = 20

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 = 20 + 2.25

Reorder the terms:
2.25 + -3a + a2 = 20 + 2.25

Combine like terms: 20 + 2.25 = 22.25
2.25 + -3a + a2 = 22.25

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(a + -1.5) equal to 4.716990566 and -4.716990566.

Subproblem 1

a + -1.5 = 4.716990566 Simplifying a + -1.5 = 4.716990566 Reorder the terms: -1.5 + a = 4.716990566 Solving -1.5 + a = 4.716990566 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 = 4.716990566 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 4.716990566 + 1.5 a = 4.716990566 + 1.5 Combine like terms: 4.716990566 + 1.5 = 6.216990566 a = 6.216990566 Simplifying a = 6.216990566

Subproblem 2

a + -1.5 = -4.716990566 Simplifying a + -1.5 = -4.716990566 Reorder the terms: -1.5 + a = -4.716990566 Solving -1.5 + a = -4.716990566 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 = -4.716990566 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -4.716990566 + 1.5 a = -4.716990566 + 1.5 Combine like terms: -4.716990566 + 1.5 = -3.216990566 a = -3.216990566 Simplifying a = -3.216990566

Solution

The solution to the problem is based on the solutions from the subproblems. a = {6.216990566, -3.216990566}

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