30a+a^2=(60-2a)-20

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Solution for 30a+a^2=(60-2a)-20 equation:


Simplifying
30a + a2 = (60 + -2a) + -20

Remove parenthesis around (60 + -2a)
30a + a2 = 60 + -2a + -20

Reorder the terms:
30a + a2 = 60 + -20 + -2a

Combine like terms: 60 + -20 = 40
30a + a2 = 40 + -2a

Solving
30a + a2 = 40 + -2a

Solving for variable 'a'.

Reorder the terms:
-40 + 30a + 2a + a2 = 40 + -2a + -40 + 2a

Combine like terms: 30a + 2a = 32a
-40 + 32a + a2 = 40 + -2a + -40 + 2a

Reorder the terms:
-40 + 32a + a2 = 40 + -40 + -2a + 2a

Combine like terms: 40 + -40 = 0
-40 + 32a + a2 = 0 + -2a + 2a
-40 + 32a + a2 = -2a + 2a

Combine like terms: -2a + 2a = 0
-40 + 32a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 32a + 40 + a2 = 0 + 40

Reorder the terms:
-40 + 40 + 32a + a2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 32a + a2 = 0 + 40
32a + a2 = 0 + 40

Combine like terms: 0 + 40 = 40
32a + a2 = 40

The a term is 32a.  Take half its coefficient (16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
32a + 256 + a2 = 40 + 256

Reorder the terms:
256 + 32a + a2 = 40 + 256

Combine like terms: 40 + 256 = 296
256 + 32a + a2 = 296

Factor a perfect square on the left side:
(a + 16)(a + 16) = 296

Calculate the square root of the right side: 17.204650534

Break this problem into two subproblems by setting 
(a + 16) equal to 17.204650534 and -17.204650534.

Subproblem 1

a + 16 = 17.204650534 Simplifying a + 16 = 17.204650534 Reorder the terms: 16 + a = 17.204650534 Solving 16 + a = 17.204650534 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + a = 17.204650534 + -16 Combine like terms: 16 + -16 = 0 0 + a = 17.204650534 + -16 a = 17.204650534 + -16 Combine like terms: 17.204650534 + -16 = 1.204650534 a = 1.204650534 Simplifying a = 1.204650534

Subproblem 2

a + 16 = -17.204650534 Simplifying a + 16 = -17.204650534 Reorder the terms: 16 + a = -17.204650534 Solving 16 + a = -17.204650534 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + a = -17.204650534 + -16 Combine like terms: 16 + -16 = 0 0 + a = -17.204650534 + -16 a = -17.204650534 + -16 Combine like terms: -17.204650534 + -16 = -33.204650534 a = -33.204650534 Simplifying a = -33.204650534

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.204650534, -33.204650534}

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