240=480x-2x^2

Simple and best practice solution for 240=480x-2x^2 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 240=480x-2x^2 equation: 


Simplifying
240 = 480x + -2x2

Solving
240 = 480x + -2x2

Solving for variable 'x'.

Reorder the terms:
240 + -480x + 2x2 = 480x + -480x + -2x2 + 2x2

Combine like terms: 480x + -480x = 0
240 + -480x + 2x2 = 0 + -2x2 + 2x2
240 + -480x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
240 + -480x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(120 + -240x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(120 + -240x + x2)' equal to zero and attempt to solve:

Simplifying
120 + -240x + x2 = 0

Solving
120 + -240x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-120' to each side of the equation.
120 + -240x + -120 + x2 = 0 + -120

Reorder the terms:
120 + -120 + -240x + x2 = 0 + -120

Combine like terms: 120 + -120 = 0
0 + -240x + x2 = 0 + -120
-240x + x2 = 0 + -120

Combine like terms: 0 + -120 = -120
-240x + x2 = -120

The x term is -240x.  Take half its coefficient (-120).
Square it (14400) and add it to both sides.

Add '14400' to each side of the equation.
-240x + 14400 + x2 = -120 + 14400

Reorder the terms:
14400 + -240x + x2 = -120 + 14400

Combine like terms: -120 + 14400 = 14280
14400 + -240x + x2 = 14280

Factor a perfect square on the left side:
(x + -120)(x + -120) = 14280

Calculate the square root of the right side: 119.49895397

Break this problem into two subproblems by setting 
(x + -120) equal to 119.49895397 and -119.49895397.


Subproblem 1
x + -120 = 119.49895397

Simplifying
x + -120 = 119.49895397

Reorder the terms:
-120 + x = 119.49895397

Solving
-120 + x = 119.49895397

Solving for variable 'x'.

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

Add '120' to each side of the equation.
-120 + 120 + x = 119.49895397 + 120

Combine like terms: -120 + 120 = 0
0 + x = 119.49895397 + 120
x = 119.49895397 + 120

Combine like terms: 119.49895397 + 120 = 239.49895397
x = 239.49895397

Simplifying
x = 239.49895397


Subproblem 2
x + -120 = -119.49895397

Simplifying
x + -120 = -119.49895397

Reorder the terms:
-120 + x = -119.49895397

Solving
-120 + x = -119.49895397

Solving for variable 'x'.

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

Add '120' to each side of the equation.
-120 + 120 + x = -119.49895397 + 120

Combine like terms: -120 + 120 = 0
0 + x = -119.49895397 + 120
x = -119.49895397 + 120

Combine like terms: -119.49895397 + 120 = 0.50104603
x = 0.50104603

Simplifying
x = 0.50104603


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {239.49895397, 0.50104603}
Solution
x = {239.49895397, 0.50104603}

See similar equations:

| 120=480x-2x^2 | | (2x-9)=(3x-28) | | 3e^2x=24 | | 100=480x-2x^2 | | 4(-7+5b)=20+4b | | 2x+3y+6z=48 | | -16x^2+80x-0=0 | | -(7a-8)=3a-22 | | x-2y=102 | | 3x+18+3x+18+3x+18=180 | | 6x-20=-4-2(4-7x) | | 5n+18=3n+26 | | -n+40=3(5n+8) | | 3(1+5r)=5r+23 | | 10x^2-9x=2x+6 | | 2(4-5p)=-8p | | -(r+6)=22-5r | | -4x-24=32 | | -16=4v | | -6(8+2m)=-3(4+m) | | 4w+14=54 | | 30+8v=6(5+8v) | | -9=3+4u | | 2(x-1)+2=26 | | X-1+1-8x=5(x+4)-2(2x+2) | | 6-8(6+8v)=23+v | | 6ab+6ac= | | (x-y)dy+(y)dx=0 | | 2(x+2.3)=7.2 | | 3(3y+4)=9 | | 1200x3/4 | | 3cosx=2secx |

Equations solver categories