a^2+20a+68=0

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Solution for a^2+20a+68=0 equation:


Simplifying
a2 + 20a + 68 = 0

Reorder the terms:
68 + 20a + a2 = 0

Solving
68 + 20a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-68' to each side of the equation.
68 + 20a + -68 + a2 = 0 + -68

Reorder the terms:
68 + -68 + 20a + a2 = 0 + -68

Combine like terms: 68 + -68 = 0
0 + 20a + a2 = 0 + -68
20a + a2 = 0 + -68

Combine like terms: 0 + -68 = -68
20a + a2 = -68

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 = -68 + 100

Reorder the terms:
100 + 20a + a2 = -68 + 100

Combine like terms: -68 + 100 = 32
100 + 20a + a2 = 32

Factor a perfect square on the left side:
(a + 10)(a + 10) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(a + 10) equal to 5.656854249 and -5.656854249.

Subproblem 1

a + 10 = 5.656854249 Simplifying a + 10 = 5.656854249 Reorder the terms: 10 + a = 5.656854249 Solving 10 + a = 5.656854249 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 = 5.656854249 + -10 Combine like terms: 10 + -10 = 0 0 + a = 5.656854249 + -10 a = 5.656854249 + -10 Combine like terms: 5.656854249 + -10 = -4.343145751 a = -4.343145751 Simplifying a = -4.343145751

Subproblem 2

a + 10 = -5.656854249 Simplifying a + 10 = -5.656854249 Reorder the terms: 10 + a = -5.656854249 Solving 10 + a = -5.656854249 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 = -5.656854249 + -10 Combine like terms: 10 + -10 = 0 0 + a = -5.656854249 + -10 a = -5.656854249 + -10 Combine like terms: -5.656854249 + -10 = -15.656854249 a = -15.656854249 Simplifying a = -15.656854249

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-4.343145751, -15.656854249}

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