3A^2-30A+54=0

Simple and best practice solution for 3A^2-30A+54=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^2-30A+54=0 equation: 


Simplifying
3A2 + -30A + 54 = 0

Reorder the terms:
54 + -30A + 3A2 = 0

Solving
54 + -30A + 3A2 = 0

Solving for variable 'A'.

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + -10A + A2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(18 + -10A + A2)' equal to zero and attempt to solve:

Simplifying
18 + -10A + A2 = 0

Solving
18 + -10A + A2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -10A + -18 + A2 = 0 + -18

Reorder the terms:
18 + -18 + -10A + A2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -10A + A2 = 0 + -18
-10A + A2 = 0 + -18

Combine like terms: 0 + -18 = -18
-10A + A2 = -18

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 = -18 + 25

Reorder the terms:
25 + -10A + A2 = -18 + 25

Combine like terms: -18 + 25 = 7
25 + -10A + A2 = 7

Factor a perfect square on the left side:
(A + -5)(A + -5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(A + -5) equal to 2.645751311 and -2.645751311.


Subproblem 1
A + -5 = 2.645751311

Simplifying
A + -5 = 2.645751311

Reorder the terms:
-5 + A = 2.645751311

Solving
-5 + A = 2.645751311

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 = 2.645751311 + 5

Combine like terms: -5 + 5 = 0
0 + A = 2.645751311 + 5
A = 2.645751311 + 5

Combine like terms: 2.645751311 + 5 = 7.645751311
A = 7.645751311

Simplifying
A = 7.645751311


Subproblem 2
A + -5 = -2.645751311

Simplifying
A + -5 = -2.645751311

Reorder the terms:
-5 + A = -2.645751311

Solving
-5 + A = -2.645751311

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 = -2.645751311 + 5

Combine like terms: -5 + 5 = 0
0 + A = -2.645751311 + 5
A = -2.645751311 + 5

Combine like terms: -2.645751311 + 5 = 2.354248689
A = 2.354248689

Simplifying
A = 2.354248689


Solution
The solution to the problem is based on the solutions
from the subproblems.
A = {7.645751311, 2.354248689}
Solution
A = {7.645751311, 2.354248689}

See similar equations:

| 2x-8=16-x | | -7=7d+21 | | n^2=-3n+4 | | 9x-3-6x=-3+9x | | x^2-10x+5=29 | | 9(12+4z)=-54 | | =(8x^2y-3xy+7xy^2)-(5x^2y+3xy+2xy^2) | | -2(2b+2)+(5b-4)=0 | | (-3d+10)(2d-1)= | | 6x-3G=9 | | 3x^5-7x+2x^6= | | x^2=-36+12x | | 3.5x=3x+10 | | 8(2.5-3/4)-20=a | | 2(a-3)=5(4-3a) | | 8(2.5-3/4)-20= | | m^2-24=5m | | -(0.75)y=-0.625 | | (2z-7)(-1z+3)= | | 3x^2-8=100 | | 2(x+3)(x-1)=234 | | x^2-24x=-44 | | (-1p+2)(3p^2+1)= | | 3(4.8)+y=3y | | 3t-3+2t=7t-15 | | 3.4q-5.6-3.2q=-0.8q-3.9 | | 144=x(x+2)3 | | (6-5n)(6+5n)= | | 5*(2b-14)=5*b+1 | | 4b^2-8b=0 | | 6i^28=6 | | 2*m+11=4*m*11 |

Equations solver categories