36x^2-216x+240=0

Simple and best practice solution for 36x^2-216x+240=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 36x^2-216x+240=0 equation: 


Simplifying
36x2 + -216x + 240 = 0

Reorder the terms:
240 + -216x + 36x2 = 0

Solving
240 + -216x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(20 + -18x + 3x2) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(20 + -18x + 3x2)' equal to zero and attempt to solve:

Simplifying
20 + -18x + 3x2 = 0

Solving
20 + -18x + 3x2 = 0

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

Divide each side by '3'.
6.666666667 + -6x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + -6x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + -6x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + -6x + x2 = 0 + -6.666666667
-6x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
-6x + x2 = -6.666666667

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -6.666666667 + 9

Reorder the terms:
9 + -6x + x2 = -6.666666667 + 9

Combine like terms: -6.666666667 + 9 = 2.333333333
9 + -6x + x2 = 2.333333333

Factor a perfect square on the left side:
(x + -3)(x + -3) = 2.333333333

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(x + -3) equal to 1.527525232 and -1.527525232.


Subproblem 1
x + -3 = 1.527525232

Simplifying
x + -3 = 1.527525232

Reorder the terms:
-3 + x = 1.527525232

Solving
-3 + x = 1.527525232

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 1.527525232 + 3

Combine like terms: -3 + 3 = 0
0 + x = 1.527525232 + 3
x = 1.527525232 + 3

Combine like terms: 1.527525232 + 3 = 4.527525232
x = 4.527525232

Simplifying
x = 4.527525232


Subproblem 2
x + -3 = -1.527525232

Simplifying
x + -3 = -1.527525232

Reorder the terms:
-3 + x = -1.527525232

Solving
-3 + x = -1.527525232

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -1.527525232 + 3

Combine like terms: -3 + 3 = 0
0 + x = -1.527525232 + 3
x = -1.527525232 + 3

Combine like terms: -1.527525232 + 3 = 1.472474768
x = 1.472474768

Simplifying
x = 1.472474768


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.527525232, 1.472474768}
Solution
x = {4.527525232, 1.472474768}

See similar equations:

| s+(s+6)+2s=25 | | 9v^2+55v-4=4+2v^2 | | M+5m+8m-2= | | 1120/350 | | 2x^2-14=27x | | (4x+5)+(15x-3)= | | 2×​5/12 | | 18=-1(-8z-2) | | -56=-2x-22 | | 24x+144+x^2=0 | | 2(5x-3)=x-3 | | 16x+64+x^2=0 | | q^2+13q+36=0 | | 15y-13y=14 | | 2.55x=17.85 | | 5k+5k=10 | | -x+11y=-1 | | 15r-13r=10 | | 2(2x+6)=188 | | 10y-5y=20 | | X-5/39 | | 16v^2+20=5v | | 20y-5y=20 | | (x+1)-(x-1)=[(x+1)+4]-(2x+2x) | | 5x+10y=3000 | | 5(3+z)=75 | | 10y-5y=30 | | 2(x+8)=(4x+16) | | 9x^2-30x+10=0 | | 5h+h=18 | | (8x-2)/2 | | k^2-18k+50=0 |

Equations solver categories