100x-2x^2=100+2x

Simple and best practice solution for 100x-2x^2=100+2x 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 100x-2x^2=100+2x equation: 


Simplifying
100x + -2x2 = 100 + 2x

Solving
100x + -2x2 = 100 + 2x

Solving for variable 'x'.

Reorder the terms:
-100 + 100x + -2x + -2x2 = 100 + 2x + -100 + -2x

Combine like terms: 100x + -2x = 98x
-100 + 98x + -2x2 = 100 + 2x + -100 + -2x

Reorder the terms:
-100 + 98x + -2x2 = 100 + -100 + 2x + -2x

Combine like terms: 100 + -100 = 0
-100 + 98x + -2x2 = 0 + 2x + -2x
-100 + 98x + -2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-100 + 98x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 49x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-50 + 49x + -1x2)' equal to zero and attempt to solve:

Simplifying
-50 + 49x + -1x2 = 0

Solving
-50 + 49x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
50 + -49x + x2 = 0

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + -49x + -50 + x2 = 0 + -50

Reorder the terms:
50 + -50 + -49x + x2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -49x + x2 = 0 + -50
-49x + x2 = 0 + -50

Combine like terms: 0 + -50 = -50
-49x + x2 = -50

The x term is -49x.  Take half its coefficient (-24.5).
Square it (600.25) and add it to both sides.

Add '600.25' to each side of the equation.
-49x + 600.25 + x2 = -50 + 600.25

Reorder the terms:
600.25 + -49x + x2 = -50 + 600.25

Combine like terms: -50 + 600.25 = 550.25
600.25 + -49x + x2 = 550.25

Factor a perfect square on the left side:
(x + -24.5)(x + -24.5) = 550.25

Calculate the square root of the right side: 23.457408211

Break this problem into two subproblems by setting 
(x + -24.5) equal to 23.457408211 and -23.457408211.


Subproblem 1
x + -24.5 = 23.457408211

Simplifying
x + -24.5 = 23.457408211

Reorder the terms:
-24.5 + x = 23.457408211

Solving
-24.5 + x = 23.457408211

Solving for variable 'x'.

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

Add '24.5' to each side of the equation.
-24.5 + 24.5 + x = 23.457408211 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + x = 23.457408211 + 24.5
x = 23.457408211 + 24.5

Combine like terms: 23.457408211 + 24.5 = 47.957408211
x = 47.957408211

Simplifying
x = 47.957408211


Subproblem 2
x + -24.5 = -23.457408211

Simplifying
x + -24.5 = -23.457408211

Reorder the terms:
-24.5 + x = -23.457408211

Solving
-24.5 + x = -23.457408211

Solving for variable 'x'.

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

Add '24.5' to each side of the equation.
-24.5 + 24.5 + x = -23.457408211 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + x = -23.457408211 + 24.5
x = -23.457408211 + 24.5

Combine like terms: -23.457408211 + 24.5 = 1.042591789
x = 1.042591789

Simplifying
x = 1.042591789


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {47.957408211, 1.042591789}
Solution
x = {47.957408211, 1.042591789}

See similar equations:

| 84/24 | | 100x-2x^2=100+x | | 3(2x-1)+4=3x-5 | | 2/3=7 | | -3(d+11)=15 | | 3x^2-2y-8= | | 3a^2b+3ab^2+3ab^2= | | 2(4x-3)-8=42x | | 7=((2x)/(0.42-x)) | | 7=(2x/.42-x) | | (2+3i)(x+yi)=16+11i | | 9x^2+ax-5=0 | | (X+2)(3x-5)=0 | | 12=3x-18 | | 2-9y=-2 | | C=√64/25×√9/6 | | C=√64/25×√9/6= | | 20+[16-1]3-4= | | 20+4a=-6 | | X=1-5/4×2/15 | | 8-3u=39 | | abs(3x-2)=x+4 | | x^4+6x^2-8=0 | | 24.78/4.2 | | 0.01x^2-0.1x-0.3=0 | | 25y+5y=x | | lx-1l=3x | | 5(y+2)=4(x+3) | | -0.01x^2-0.1x-0.03=0 | | 25y+5=x | | 8+x=23 | | -4X+2X=0 |

Equations solver categories