2a^2+4a-20=

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Solution for 2a^2+4a-20= equation: 


Simplifying
2a2 + 4a + -20 = 0

Reorder the terms:
-20 + 4a + 2a2 = 0

Solving
-20 + 4a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 2a + a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + 2a + a2)' equal to zero and attempt to solve:

Simplifying
-10 + 2a + a2 = 0

Solving
-10 + 2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 2a + 10 + a2 = 0 + 10

Reorder the terms:
-10 + 10 + 2a + a2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 2a + a2 = 0 + 10
2a + a2 = 0 + 10

Combine like terms: 0 + 10 = 10
2a + a2 = 10

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = 10 + 1

Reorder the terms:
1 + 2a + a2 = 10 + 1

Combine like terms: 10 + 1 = 11
1 + 2a + a2 = 11

Factor a perfect square on the left side:
(a + 1)(a + 1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(a + 1) equal to 3.31662479 and -3.31662479.


Subproblem 1
a + 1 = 3.31662479

Simplifying
a + 1 = 3.31662479

Reorder the terms:
1 + a = 3.31662479

Solving
1 + a = 3.31662479

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = 3.31662479 + -1

Combine like terms: 1 + -1 = 0
0 + a = 3.31662479 + -1
a = 3.31662479 + -1

Combine like terms: 3.31662479 + -1 = 2.31662479
a = 2.31662479

Simplifying
a = 2.31662479


Subproblem 2
a + 1 = -3.31662479

Simplifying
a + 1 = -3.31662479

Reorder the terms:
1 + a = -3.31662479

Solving
1 + a = -3.31662479

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = -3.31662479 + -1

Combine like terms: 1 + -1 = 0
0 + a = -3.31662479 + -1
a = -3.31662479 + -1

Combine like terms: -3.31662479 + -1 = -4.31662479
a = -4.31662479

Simplifying
a = -4.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.31662479, -4.31662479}
Solution
a = {2.31662479, -4.31662479}

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