a^2+2a=5

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Solution for a^2+2a=5 equation:


Simplifying
a2 + 2a = 5

Reorder the terms:
2a + a2 = 5

Solving
2a + a2 = 5

Solving for variable 'a'.

Reorder the terms:
-5 + 2a + a2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 2a + 5 + a2 = 0 + 5

Reorder the terms:
-5 + 5 + 2a + a2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2a + a2 = 0 + 5
2a + a2 = 0 + 5

Combine like terms: 0 + 5 = 5
2a + a2 = 5

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 = 5 + 1

Reorder the terms:
1 + 2a + a2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + 2a + a2 = 6

Factor a perfect square on the left side:
(a + 1)(a + 1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(a + 1) equal to 2.449489743 and -2.449489743.

Subproblem 1

a + 1 = 2.449489743 Simplifying a + 1 = 2.449489743 Reorder the terms: 1 + a = 2.449489743 Solving 1 + a = 2.449489743 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 = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + a = 2.449489743 + -1 a = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 a = 1.449489743 Simplifying a = 1.449489743

Subproblem 2

a + 1 = -2.449489743 Simplifying a + 1 = -2.449489743 Reorder the terms: 1 + a = -2.449489743 Solving 1 + a = -2.449489743 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 = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + a = -2.449489743 + -1 a = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 a = -3.449489743 Simplifying a = -3.449489743

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.449489743, -3.449489743}

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