a^2+160a+160=0

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Solution for a^2+160a+160=0 equation:


Simplifying
a2 + 160a + 160 = 0

Reorder the terms:
160 + 160a + a2 = 0

Solving
160 + 160a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-160' to each side of the equation.
160 + 160a + -160 + a2 = 0 + -160

Reorder the terms:
160 + -160 + 160a + a2 = 0 + -160

Combine like terms: 160 + -160 = 0
0 + 160a + a2 = 0 + -160
160a + a2 = 0 + -160

Combine like terms: 0 + -160 = -160
160a + a2 = -160

The a term is 160a.  Take half its coefficient (80).
Square it (6400) and add it to both sides.

Add '6400' to each side of the equation.
160a + 6400 + a2 = -160 + 6400

Reorder the terms:
6400 + 160a + a2 = -160 + 6400

Combine like terms: -160 + 6400 = 6240
6400 + 160a + a2 = 6240

Factor a perfect square on the left side:
(a + 80)(a + 80) = 6240

Calculate the square root of the right side: 78.993670633

Break this problem into two subproblems by setting 
(a + 80) equal to 78.993670633 and -78.993670633.

Subproblem 1

a + 80 = 78.993670633 Simplifying a + 80 = 78.993670633 Reorder the terms: 80 + a = 78.993670633 Solving 80 + a = 78.993670633 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + a = 78.993670633 + -80 Combine like terms: 80 + -80 = 0 0 + a = 78.993670633 + -80 a = 78.993670633 + -80 Combine like terms: 78.993670633 + -80 = -1.006329367 a = -1.006329367 Simplifying a = -1.006329367

Subproblem 2

a + 80 = -78.993670633 Simplifying a + 80 = -78.993670633 Reorder the terms: 80 + a = -78.993670633 Solving 80 + a = -78.993670633 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + a = -78.993670633 + -80 Combine like terms: 80 + -80 = 0 0 + a = -78.993670633 + -80 a = -78.993670633 + -80 Combine like terms: -78.993670633 + -80 = -158.993670633 a = -158.993670633 Simplifying a = -158.993670633

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-1.006329367, -158.993670633}

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