a^2+2a=238

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Solution for a^2+2a=238 equation:


Simplifying
a2 + 2a = 238

Reorder the terms:
2a + a2 = 238

Solving
2a + a2 = 238

Solving for variable 'a'.

Reorder the terms:
-238 + 2a + a2 = 238 + -238

Combine like terms: 238 + -238 = 0
-238 + 2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '238' to each side of the equation.
-238 + 2a + 238 + a2 = 0 + 238

Reorder the terms:
-238 + 238 + 2a + a2 = 0 + 238

Combine like terms: -238 + 238 = 0
0 + 2a + a2 = 0 + 238
2a + a2 = 0 + 238

Combine like terms: 0 + 238 = 238
2a + a2 = 238

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 = 238 + 1

Reorder the terms:
1 + 2a + a2 = 238 + 1

Combine like terms: 238 + 1 = 239
1 + 2a + a2 = 239

Factor a perfect square on the left side:
(a + 1)(a + 1) = 239

Calculate the square root of the right side: 15.459624834

Break this problem into two subproblems by setting 
(a + 1) equal to 15.459624834 and -15.459624834.

Subproblem 1

a + 1 = 15.459624834 Simplifying a + 1 = 15.459624834 Reorder the terms: 1 + a = 15.459624834 Solving 1 + a = 15.459624834 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 = 15.459624834 + -1 Combine like terms: 1 + -1 = 0 0 + a = 15.459624834 + -1 a = 15.459624834 + -1 Combine like terms: 15.459624834 + -1 = 14.459624834 a = 14.459624834 Simplifying a = 14.459624834

Subproblem 2

a + 1 = -15.459624834 Simplifying a + 1 = -15.459624834 Reorder the terms: 1 + a = -15.459624834 Solving 1 + a = -15.459624834 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 = -15.459624834 + -1 Combine like terms: 1 + -1 = 0 0 + a = -15.459624834 + -1 a = -15.459624834 + -1 Combine like terms: -15.459624834 + -1 = -16.459624834 a = -16.459624834 Simplifying a = -16.459624834

Solution

The solution to the problem is based on the solutions from the subproblems. a = {14.459624834, -16.459624834}

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