a^2+6a=10

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Solution for a^2+6a=10 equation:


Simplifying
a2 + 6a = 10

Reorder the terms:
6a + a2 = 10

Solving
6a + a2 = 10

Solving for variable 'a'.

Reorder the terms:
-10 + 6a + a2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 6a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 6a + 10 + a2 = 0 + 10

Reorder the terms:
-10 + 10 + 6a + a2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 6a + a2 = 0 + 10
6a + a2 = 0 + 10

Combine like terms: 0 + 10 = 10
6a + a2 = 10

The a term is 6a.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6a + 9 + a2 = 10 + 9

Reorder the terms:
9 + 6a + a2 = 10 + 9

Combine like terms: 10 + 9 = 19
9 + 6a + a2 = 19

Factor a perfect square on the left side:
(a + 3)(a + 3) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(a + 3) equal to 4.358898944 and -4.358898944.

Subproblem 1

a + 3 = 4.358898944 Simplifying a + 3 = 4.358898944 Reorder the terms: 3 + a = 4.358898944 Solving 3 + a = 4.358898944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 4.358898944 + -3 Combine like terms: 3 + -3 = 0 0 + a = 4.358898944 + -3 a = 4.358898944 + -3 Combine like terms: 4.358898944 + -3 = 1.358898944 a = 1.358898944 Simplifying a = 1.358898944

Subproblem 2

a + 3 = -4.358898944 Simplifying a + 3 = -4.358898944 Reorder the terms: 3 + a = -4.358898944 Solving 3 + a = -4.358898944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -4.358898944 + -3 Combine like terms: 3 + -3 = 0 0 + a = -4.358898944 + -3 a = -4.358898944 + -3 Combine like terms: -4.358898944 + -3 = -7.358898944 a = -7.358898944 Simplifying a = -7.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.358898944, -7.358898944}

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