3a^2+36a+10=0

Simple and best practice solution for 3a^2+36a+10=0 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 3a^2+36a+10=0 equation:


Simplifying
3a2 + 36a + 10 = 0

Reorder the terms:
10 + 36a + 3a2 = 0

Solving
10 + 36a + 3a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
3.333333333 + 12a + a2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + 12a + -3.333333333 + a2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + 12a + a2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + 12a + a2 = 0 + -3.333333333
12a + a2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
12a + a2 = -3.333333333

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 = -3.333333333 + 36

Reorder the terms:
36 + 12a + a2 = -3.333333333 + 36

Combine like terms: -3.333333333 + 36 = 32.666666667
36 + 12a + a2 = 32.666666667

Factor a perfect square on the left side:
(a + 6)(a + 6) = 32.666666667

Calculate the square root of the right side: 5.715476067

Break this problem into two subproblems by setting 
(a + 6) equal to 5.715476067 and -5.715476067.

Subproblem 1

a + 6 = 5.715476067 Simplifying a + 6 = 5.715476067 Reorder the terms: 6 + a = 5.715476067 Solving 6 + a = 5.715476067 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 = 5.715476067 + -6 Combine like terms: 6 + -6 = 0 0 + a = 5.715476067 + -6 a = 5.715476067 + -6 Combine like terms: 5.715476067 + -6 = -0.284523933 a = -0.284523933 Simplifying a = -0.284523933

Subproblem 2

a + 6 = -5.715476067 Simplifying a + 6 = -5.715476067 Reorder the terms: 6 + a = -5.715476067 Solving 6 + a = -5.715476067 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 = -5.715476067 + -6 Combine like terms: 6 + -6 = 0 0 + a = -5.715476067 + -6 a = -5.715476067 + -6 Combine like terms: -5.715476067 + -6 = -11.715476067 a = -11.715476067 Simplifying a = -11.715476067

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.284523933, -11.715476067}

See similar equations:

| 56-35x=7-7x-49 | | 6x^2-13x-12b^2=0 | | 6y^3+3y^2-3y=0 | | 6c=15+27c | | 7.8y+6=23.16 | | 10-3y-y^2=0 | | 5(t-6)+5t=5(2t+3)-9 | | 53=7x-3 | | 15x^2+14x-8=0 | | (6x-5)(2x+2)=0 | | 60-0.16x=80 | | 4+800= | | h=-16t^2+95 | | 5-5x=6x+5 | | 5m^2-4m-12=0 | | 4x-2=4x+8 | | -5n(4n-3)=0 | | 7x^2+x-6=0 | | .01(x+16)-0.16=0.01(5x+16) | | (x-3)(2x+9)=0 | | 4(5x+4)-19=17x+3 | | y=x^2-10x-5 | | 34=x+5+2x | | -9.8x=29.4 | | p+39=23 | | 2+x^2-x^4=0 | | 20(1-8r)=10(r+19) | | .1x=7 | | x-7.4=-5.6 | | x-7.4=-56 | | 9w^3(5w^3+10w)= | | (x+9)(x+5)=0 |

Equations solver categories