5a(18-4a)=-36

Simple and best practice solution for 5a(18-4a)=-36 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 5a(18-4a)=-36 equation: 


Simplifying
5a(18 + -4a) = -36
(18 * 5a + -4a * 5a) = -36
(90a + -20a2) = -36

Solving
90a + -20a2 = -36

Solving for variable 'a'.

Reorder the terms:
36 + 90a + -20a2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + 90a + -20a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + 45a + -10a2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(18 + 45a + -10a2)' equal to zero and attempt to solve:

Simplifying
18 + 45a + -10a2 = 0

Solving
18 + 45a + -10a2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-1.8 + -4.5a + a2 = 0.0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + -4.5a + 1.8 + a2 = 0.0 + 1.8

Reorder the terms:
-1.8 + 1.8 + -4.5a + a2 = 0.0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + -4.5a + a2 = 0.0 + 1.8
-4.5a + a2 = 0.0 + 1.8

Combine like terms: 0.0 + 1.8 = 1.8
-4.5a + a2 = 1.8

The a term is -4.5a.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5a + 5.0625 + a2 = 1.8 + 5.0625

Reorder the terms:
5.0625 + -4.5a + a2 = 1.8 + 5.0625

Combine like terms: 1.8 + 5.0625 = 6.8625
5.0625 + -4.5a + a2 = 6.8625

Factor a perfect square on the left side:
(a + -2.25)(a + -2.25) = 6.8625

Calculate the square root of the right side: 2.619637379

Break this problem into two subproblems by setting 
(a + -2.25) equal to 2.619637379 and -2.619637379.


Subproblem 1
a + -2.25 = 2.619637379

Simplifying
a + -2.25 = 2.619637379

Reorder the terms:
-2.25 + a = 2.619637379

Solving
-2.25 + a = 2.619637379

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '2.25' to each side of the equation.
-2.25 + 2.25 + a = 2.619637379 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + a = 2.619637379 + 2.25
a = 2.619637379 + 2.25

Combine like terms: 2.619637379 + 2.25 = 4.869637379
a = 4.869637379

Simplifying
a = 4.869637379


Subproblem 2
a + -2.25 = -2.619637379

Simplifying
a + -2.25 = -2.619637379

Reorder the terms:
-2.25 + a = -2.619637379

Solving
-2.25 + a = -2.619637379

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '2.25' to each side of the equation.
-2.25 + 2.25 + a = -2.619637379 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + a = -2.619637379 + 2.25
a = -2.619637379 + 2.25

Combine like terms: -2.619637379 + 2.25 = -0.369637379
a = -0.369637379

Simplifying
a = -0.369637379


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.869637379, -0.369637379}
Solution
a = {4.869637379, -0.369637379}

See similar equations:

| 5w-2=2w+7 | | 5x-(x-3)=4x+1 | | 14+2x+4=40 | | 12+9+x=37 | | 27-4x=-7(1+2x) | | 1.5(s+15)=2s | | 5n-20=3n+2 | | -11x+-6=-83 | | 4n-15=-n | | 5x-3+-2x-6=27 | | 256=16t^2+64t+192 | | 2y^2+8y=-40 | | 4u-15=5u+12 | | 2m+5-3m=12-4m | | 2-18x=-3(6x+2) | | 3x+5=x+20 | | 8.2x-2.1x=138 | | -2(1-8x)=18+6x | | -6(x-7)=90 | | 9y^2+13y-42=0 | | 15+19+x=41 | | 2-11x=x-33 | | 0=x*sqrt(16-x^2) | | (40+90)-40=n | | 2y+2x+2-2y(-6x-2y-5)=0 | | 6x-(3x+4)=4x-18 | | 2(3-2z)-6(2z+4)=z-30 | | 4-6a*4a=1-5(7-2a) | | 3(-.33333333333+5)=-2(3*-.33333333333-6) | | t+2T=41200 | | 3x^2=-5x+28 | | 112-88=24x |

Equations solver categories