a^2+10a-45=0

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Solution for a^2+10a-45=0 equation: 


Simplifying
a2 + 10a + -45 = 0

Reorder the terms:
-45 + 10a + a2 = 0

Solving
-45 + 10a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 10a + 45 + a2 = 0 + 45

Reorder the terms:
-45 + 45 + 10a + a2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 10a + a2 = 0 + 45
10a + a2 = 0 + 45

Combine like terms: 0 + 45 = 45
10a + a2 = 45

The a term is 10a.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10a + 25 + a2 = 45 + 25

Reorder the terms:
25 + 10a + a2 = 45 + 25

Combine like terms: 45 + 25 = 70
25 + 10a + a2 = 70

Factor a perfect square on the left side:
(a + 5)(a + 5) = 70

Calculate the square root of the right side: 8.366600265

Break this problem into two subproblems by setting 
(a + 5) equal to 8.366600265 and -8.366600265.


Subproblem 1
a + 5 = 8.366600265

Simplifying
a + 5 = 8.366600265

Reorder the terms:
5 + a = 8.366600265

Solving
5 + a = 8.366600265

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + a = 8.366600265 + -5

Combine like terms: 5 + -5 = 0
0 + a = 8.366600265 + -5
a = 8.366600265 + -5

Combine like terms: 8.366600265 + -5 = 3.366600265
a = 3.366600265

Simplifying
a = 3.366600265


Subproblem 2
a + 5 = -8.366600265

Simplifying
a + 5 = -8.366600265

Reorder the terms:
5 + a = -8.366600265

Solving
5 + a = -8.366600265

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + a = -8.366600265 + -5

Combine like terms: 5 + -5 = 0
0 + a = -8.366600265 + -5
a = -8.366600265 + -5

Combine like terms: -8.366600265 + -5 = -13.366600265
a = -13.366600265

Simplifying
a = -13.366600265


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.366600265, -13.366600265}

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