a^2+5a-27=0

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Solution for a^2+5a-27=0 equation:


Simplifying
a2 + 5a + -27 = 0

Reorder the terms:
-27 + 5a + a2 = 0

Solving
-27 + 5a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 5a + 27 + a2 = 0 + 27

Reorder the terms:
-27 + 27 + 5a + a2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 5a + a2 = 0 + 27
5a + a2 = 0 + 27

Combine like terms: 0 + 27 = 27
5a + a2 = 27

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 = 27 + 6.25

Reorder the terms:
6.25 + 5a + a2 = 27 + 6.25

Combine like terms: 27 + 6.25 = 33.25
6.25 + 5a + a2 = 33.25

Factor a perfect square on the left side:
(a + 2.5)(a + 2.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(a + 2.5) equal to 5.766281297 and -5.766281297.

Subproblem 1

a + 2.5 = 5.766281297 Simplifying a + 2.5 = 5.766281297 Reorder the terms: 2.5 + a = 5.766281297 Solving 2.5 + a = 5.766281297 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 = 5.766281297 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 5.766281297 + -2.5 a = 5.766281297 + -2.5 Combine like terms: 5.766281297 + -2.5 = 3.266281297 a = 3.266281297 Simplifying a = 3.266281297

Subproblem 2

a + 2.5 = -5.766281297 Simplifying a + 2.5 = -5.766281297 Reorder the terms: 2.5 + a = -5.766281297 Solving 2.5 + a = -5.766281297 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 = -5.766281297 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -5.766281297 + -2.5 a = -5.766281297 + -2.5 Combine like terms: -5.766281297 + -2.5 = -8.266281297 a = -8.266281297 Simplifying a = -8.266281297

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.266281297, -8.266281297}

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