4x^2-108x+360=0

Simple and best practice solution for 4x^2-108x+360=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 4x^2-108x+360=0 equation: 


Simplifying
4x2 + -108x + 360 = 0

Reorder the terms:
360 + -108x + 4x2 = 0

Solving
360 + -108x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(90 + -27x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(90 + -27x + x2)' equal to zero and attempt to solve:

Simplifying
90 + -27x + x2 = 0

Solving
90 + -27x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-90' to each side of the equation.
90 + -27x + -90 + x2 = 0 + -90

Reorder the terms:
90 + -90 + -27x + x2 = 0 + -90

Combine like terms: 90 + -90 = 0
0 + -27x + x2 = 0 + -90
-27x + x2 = 0 + -90

Combine like terms: 0 + -90 = -90
-27x + x2 = -90

The x term is -27x.  Take half its coefficient (-13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
-27x + 182.25 + x2 = -90 + 182.25

Reorder the terms:
182.25 + -27x + x2 = -90 + 182.25

Combine like terms: -90 + 182.25 = 92.25
182.25 + -27x + x2 = 92.25

Factor a perfect square on the left side:
(x + -13.5)(x + -13.5) = 92.25

Calculate the square root of the right side: 9.604686356

Break this problem into two subproblems by setting 
(x + -13.5) equal to 9.604686356 and -9.604686356.


Subproblem 1
x + -13.5 = 9.604686356

Simplifying
x + -13.5 = 9.604686356

Reorder the terms:
-13.5 + x = 9.604686356

Solving
-13.5 + x = 9.604686356

Solving for variable 'x'.

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

Add '13.5' to each side of the equation.
-13.5 + 13.5 + x = 9.604686356 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + x = 9.604686356 + 13.5
x = 9.604686356 + 13.5

Combine like terms: 9.604686356 + 13.5 = 23.104686356
x = 23.104686356

Simplifying
x = 23.104686356


Subproblem 2
x + -13.5 = -9.604686356

Simplifying
x + -13.5 = -9.604686356

Reorder the terms:
-13.5 + x = -9.604686356

Solving
-13.5 + x = -9.604686356

Solving for variable 'x'.

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

Add '13.5' to each side of the equation.
-13.5 + 13.5 + x = -9.604686356 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + x = -9.604686356 + 13.5
x = -9.604686356 + 13.5

Combine like terms: -9.604686356 + 13.5 = 3.895313644
x = 3.895313644

Simplifying
x = 3.895313644


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.104686356, 3.895313644}
Solution
x = {23.104686356, 3.895313644}

See similar equations:

| log(8)=2 | | 2x/8-4=16 | | 3(3+6x)-1=62 | | ln(N)=8+1.5t | | 6x-7y=840 | | (2w-3)(w)=14 | | 0.8x+0.6x=4.2 | | (1/x)-(1/3*x)=6 | | (1/x)-(1/3x)=(1/6) | | 5s-29=-31+6s | | -0.2=-0.6u+0.5u | | sqrt(2x+5)-sqrt(x+14)=-1 | | (k+4)(k-8)= | | n(n-7)+3=9 | | k-16= | | 1/5*2/7*1/3 | | in(3x-5)=1.2 | | 6.3x-5+x-1.5= | | 3x^2-56x+100=0 | | 3(3+2x)-4=29 | | 27.00+1.00x= | | (6-4i)/(1-6i) | | 10n+2=32 | | 3/xz^6-5/xz^6 | | 8-(w+10)=-9 | | 22x+x^2=520 | | 2(6s-6)=0 | | 16x-7y=(-11) | | 0.06x+x=700 | | -75+z=-75-z | | c+c+3=57 | | log(9)x=-2 |

Equations solver categories