a^2+5a-18=0

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Solution for a^2+5a-18=0 equation: 


Simplifying
a2 + 5a + -18 = 0

Reorder the terms:
-18 + 5a + a2 = 0

Solving
-18 + 5a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 5a + 18 + a2 = 0 + 18

Reorder the terms:
-18 + 18 + 5a + a2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 5a + a2 = 0 + 18
5a + a2 = 0 + 18

Combine like terms: 0 + 18 = 18
5a + a2 = 18

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 = 18 + 6.25

Reorder the terms:
6.25 + 5a + a2 = 18 + 6.25

Combine like terms: 18 + 6.25 = 24.25
6.25 + 5a + a2 = 24.25

Factor a perfect square on the left side:
(a + 2.5)(a + 2.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(a + 2.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
a + 2.5 = 4.924428901

Simplifying
a + 2.5 = 4.924428901

Reorder the terms:
2.5 + a = 4.924428901

Solving
2.5 + a = 4.924428901

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 = 4.924428901 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + a = 4.924428901 + -2.5
a = 4.924428901 + -2.5

Combine like terms: 4.924428901 + -2.5 = 2.424428901
a = 2.424428901

Simplifying
a = 2.424428901


Subproblem 2
a + 2.5 = -4.924428901

Simplifying
a + 2.5 = -4.924428901

Reorder the terms:
2.5 + a = -4.924428901

Solving
2.5 + a = -4.924428901

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 = -4.924428901 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + a = -4.924428901 + -2.5
a = -4.924428901 + -2.5

Combine like terms: -4.924428901 + -2.5 = -7.424428901
a = -7.424428901

Simplifying
a = -7.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.424428901, -7.424428901}

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