a^2+20a+46=0

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Solution for a^2+20a+46=0 equation:


Simplifying
a2 + 20a + 46 = 0

Reorder the terms:
46 + 20a + a2 = 0

Solving
46 + 20a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-46' to each side of the equation.
46 + 20a + -46 + a2 = 0 + -46

Reorder the terms:
46 + -46 + 20a + a2 = 0 + -46

Combine like terms: 46 + -46 = 0
0 + 20a + a2 = 0 + -46
20a + a2 = 0 + -46

Combine like terms: 0 + -46 = -46
20a + a2 = -46

The a term is 20a.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20a + 100 + a2 = -46 + 100

Reorder the terms:
100 + 20a + a2 = -46 + 100

Combine like terms: -46 + 100 = 54
100 + 20a + a2 = 54

Factor a perfect square on the left side:
(a + 10)(a + 10) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(a + 10) equal to 7.348469228 and -7.348469228.

Subproblem 1

a + 10 = 7.348469228 Simplifying a + 10 = 7.348469228 Reorder the terms: 10 + a = 7.348469228 Solving 10 + a = 7.348469228 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + a = 7.348469228 + -10 Combine like terms: 10 + -10 = 0 0 + a = 7.348469228 + -10 a = 7.348469228 + -10 Combine like terms: 7.348469228 + -10 = -2.651530772 a = -2.651530772 Simplifying a = -2.651530772

Subproblem 2

a + 10 = -7.348469228 Simplifying a + 10 = -7.348469228 Reorder the terms: 10 + a = -7.348469228 Solving 10 + a = -7.348469228 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + a = -7.348469228 + -10 Combine like terms: 10 + -10 = 0 0 + a = -7.348469228 + -10 a = -7.348469228 + -10 Combine like terms: -7.348469228 + -10 = -17.348469228 a = -17.348469228 Simplifying a = -17.348469228

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-2.651530772, -17.348469228}

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