a^2+12a=3

Simple and best practice solution for a^2+12a=3 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for a^2+12a=3 equation:


Simplifying
a2 + 12a = 3

Reorder the terms:
12a + a2 = 3

Solving
12a + a2 = 3

Solving for variable 'a'.

Reorder the terms:
-3 + 12a + a2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 12a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 12a + 3 + a2 = 0 + 3

Reorder the terms:
-3 + 3 + 12a + a2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 12a + a2 = 0 + 3
12a + a2 = 0 + 3

Combine like terms: 0 + 3 = 3
12a + a2 = 3

The a term is 12a.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12a + 36 + a2 = 3 + 36

Reorder the terms:
36 + 12a + a2 = 3 + 36

Combine like terms: 3 + 36 = 39
36 + 12a + a2 = 39

Factor a perfect square on the left side:
(a + 6)(a + 6) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(a + 6) equal to 6.244997998 and -6.244997998.

Subproblem 1

a + 6 = 6.244997998 Simplifying a + 6 = 6.244997998 Reorder the terms: 6 + a = 6.244997998 Solving 6 + a = 6.244997998 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = 6.244997998 + -6 Combine like terms: 6 + -6 = 0 0 + a = 6.244997998 + -6 a = 6.244997998 + -6 Combine like terms: 6.244997998 + -6 = 0.244997998 a = 0.244997998 Simplifying a = 0.244997998

Subproblem 2

a + 6 = -6.244997998 Simplifying a + 6 = -6.244997998 Reorder the terms: 6 + a = -6.244997998 Solving 6 + a = -6.244997998 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + a = -6.244997998 + -6 Combine like terms: 6 + -6 = 0 0 + a = -6.244997998 + -6 a = -6.244997998 + -6 Combine like terms: -6.244997998 + -6 = -12.244997998 a = -12.244997998 Simplifying a = -12.244997998

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.244997998, -12.244997998}

See similar equations:

| 3x-1=23+x | | 13+x=81 | | 4a+28=11a-28 | | 3(1/2)=8 | | 2-6c+9b+2c-11b+8=0 | | 1.6x-5=7.4 | | 6r=70 | | 4-8ln(x)=7 | | x^2-sqrt(2+x^2)=0 | | x-97=6 | | -3n+7+6n-2= | | 12=a+6-3a | | 4x-6/7=10 | | 20/5/4=8/n | | 8(9c-1)-10=70c+8 | | (a)v=u+10t(t) | | 90x^2-3x^3+200x+10000=0 | | 7x+6=2+3x | | -2=a+6-3a | | -9+19=-6x+5 | | 6-(-3k)= | | 6=8(c-3/4)-20 | | A+bi=-15+7i | | -10m=40 | | 86+45= | | 3.5x-20=3.5x+13 | | 2x-27=2(x+15) | | (2x-1)/3(x-2)/5-1 | | -86-45= | | 8(4s+1)=40 | | 4-2(m-6)=8 | | X+90+50=180 |

Equations solver categories