a^2+2a+1=32

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Solution for a^2+2a+1=32 equation:


Simplifying
a2 + 2a + 1 = 32

Reorder the terms:
1 + 2a + a2 = 32

Solving
1 + 2a + a2 = 32

Solving for variable 'a'.

Reorder the terms:
1 + -32 + 2a + a2 = 32 + -32

Combine like terms: 1 + -32 = -31
-31 + 2a + a2 = 32 + -32

Combine like terms: 32 + -32 = 0
-31 + 2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 2a + 31 + a2 = 0 + 31

Reorder the terms:
-31 + 31 + 2a + a2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 2a + a2 = 0 + 31
2a + a2 = 0 + 31

Combine like terms: 0 + 31 = 31
2a + a2 = 31

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 = 31 + 1

Reorder the terms:
1 + 2a + a2 = 31 + 1

Combine like terms: 31 + 1 = 32
1 + 2a + a2 = 32

Factor a perfect square on the left side:
(a + 1)(a + 1) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(a + 1) equal to 5.656854249 and -5.656854249.

Subproblem 1

a + 1 = 5.656854249 Simplifying a + 1 = 5.656854249 Reorder the terms: 1 + a = 5.656854249 Solving 1 + a = 5.656854249 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 = 5.656854249 + -1 Combine like terms: 1 + -1 = 0 0 + a = 5.656854249 + -1 a = 5.656854249 + -1 Combine like terms: 5.656854249 + -1 = 4.656854249 a = 4.656854249 Simplifying a = 4.656854249

Subproblem 2

a + 1 = -5.656854249 Simplifying a + 1 = -5.656854249 Reorder the terms: 1 + a = -5.656854249 Solving 1 + a = -5.656854249 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 = -5.656854249 + -1 Combine like terms: 1 + -1 = 0 0 + a = -5.656854249 + -1 a = -5.656854249 + -1 Combine like terms: -5.656854249 + -1 = -6.656854249 a = -6.656854249 Simplifying a = -6.656854249

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.656854249, -6.656854249}

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