a^2+10a-12=0

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Solution for a^2+10a-12=0 equation:


Simplifying
a2 + 10a + -12 = 0

Reorder the terms:
-12 + 10a + a2 = 0

Solving
-12 + 10a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 10a + 12 + a2 = 0 + 12

Reorder the terms:
-12 + 12 + 10a + a2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 10a + a2 = 0 + 12
10a + a2 = 0 + 12

Combine like terms: 0 + 12 = 12
10a + a2 = 12

The a term is 10a.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10a + 25 + a2 = 12 + 25

Reorder the terms:
25 + 10a + a2 = 12 + 25

Combine like terms: 12 + 25 = 37
25 + 10a + a2 = 37

Factor a perfect square on the left side:
(a + 5)(a + 5) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(a + 5) equal to 6.08276253 and -6.08276253.

Subproblem 1

a + 5 = 6.08276253 Simplifying a + 5 = 6.08276253 Reorder the terms: 5 + a = 6.08276253 Solving 5 + a = 6.08276253 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 6.08276253 + -5 Combine like terms: 5 + -5 = 0 0 + a = 6.08276253 + -5 a = 6.08276253 + -5 Combine like terms: 6.08276253 + -5 = 1.08276253 a = 1.08276253 Simplifying a = 1.08276253

Subproblem 2

a + 5 = -6.08276253 Simplifying a + 5 = -6.08276253 Reorder the terms: 5 + a = -6.08276253 Solving 5 + a = -6.08276253 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = -6.08276253 + -5 Combine like terms: 5 + -5 = 0 0 + a = -6.08276253 + -5 a = -6.08276253 + -5 Combine like terms: -6.08276253 + -5 = -11.08276253 a = -11.08276253 Simplifying a = -11.08276253

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.08276253, -11.08276253}

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