a^2+8a-90=0

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Solution for a^2+8a-90=0 equation: 


Simplifying
a2 + 8a + -90 = 0

Reorder the terms:
-90 + 8a + a2 = 0

Solving
-90 + 8a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 8a + 90 + a2 = 0 + 90

Reorder the terms:
-90 + 90 + 8a + a2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 8a + a2 = 0 + 90
8a + a2 = 0 + 90

Combine like terms: 0 + 90 = 90
8a + a2 = 90

The a term is 8a.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8a + 16 + a2 = 90 + 16

Reorder the terms:
16 + 8a + a2 = 90 + 16

Combine like terms: 90 + 16 = 106
16 + 8a + a2 = 106

Factor a perfect square on the left side:
(a + 4)(a + 4) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(a + 4) equal to 10.295630141 and -10.295630141.


Subproblem 1
a + 4 = 10.295630141

Simplifying
a + 4 = 10.295630141

Reorder the terms:
4 + a = 10.295630141

Solving
4 + a = 10.295630141

Solving for variable 'a'.

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

Add '-4' to each side of the equation.
4 + -4 + a = 10.295630141 + -4

Combine like terms: 4 + -4 = 0
0 + a = 10.295630141 + -4
a = 10.295630141 + -4

Combine like terms: 10.295630141 + -4 = 6.295630141
a = 6.295630141

Simplifying
a = 6.295630141


Subproblem 2
a + 4 = -10.295630141

Simplifying
a + 4 = -10.295630141

Reorder the terms:
4 + a = -10.295630141

Solving
4 + a = -10.295630141

Solving for variable 'a'.

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

Add '-4' to each side of the equation.
4 + -4 + a = -10.295630141 + -4

Combine like terms: 4 + -4 = 0
0 + a = -10.295630141 + -4
a = -10.295630141 + -4

Combine like terms: -10.295630141 + -4 = -14.295630141
a = -14.295630141

Simplifying
a = -14.295630141


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {6.295630141, -14.295630141}

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