0.01x^2+20x=3000+4x

Simple and best practice solution for 0.01x^2+20x=3000+4x 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 0.01x^2+20x=3000+4x equation:


Simplifying
0.01x2 + 20x = 3000 + 4x

Reorder the terms:
20x + 0.01x2 = 3000 + 4x

Solving
20x + 0.01x2 = 3000 + 4x

Solving for variable 'x'.

Reorder the terms:
-3000 + 20x + -4x + 0.01x2 = 3000 + 4x + -3000 + -4x

Combine like terms: 20x + -4x = 16x
-3000 + 16x + 0.01x2 = 3000 + 4x + -3000 + -4x

Reorder the terms:
-3000 + 16x + 0.01x2 = 3000 + -3000 + 4x + -4x

Combine like terms: 3000 + -3000 = 0
-3000 + 16x + 0.01x2 = 0 + 4x + -4x
-3000 + 16x + 0.01x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-3000 + 16x + 0.01x2 = 0

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

Divide each side by '0.01'.
-300000 + 1600x + x2 = 0

Move the constant term to the right:

Add '300000' to each side of the equation.
-300000 + 1600x + 300000 + x2 = 0 + 300000

Reorder the terms:
-300000 + 300000 + 1600x + x2 = 0 + 300000

Combine like terms: -300000 + 300000 = 0
0 + 1600x + x2 = 0 + 300000
1600x + x2 = 0 + 300000

Combine like terms: 0 + 300000 = 300000
1600x + x2 = 300000

The x term is 1600x.  Take half its coefficient (800).
Square it (640000) and add it to both sides.

Add '640000' to each side of the equation.
1600x + 640000 + x2 = 300000 + 640000

Reorder the terms:
640000 + 1600x + x2 = 300000 + 640000

Combine like terms: 300000 + 640000 = 940000
640000 + 1600x + x2 = 940000

Factor a perfect square on the left side:
(x + 800)(x + 800) = 940000

Calculate the square root of the right side: 969.535971483

Break this problem into two subproblems by setting 
(x + 800) equal to 969.535971483 and -969.535971483.

Subproblem 1

x + 800 = 969.535971483 Simplifying x + 800 = 969.535971483 Reorder the terms: 800 + x = 969.535971483 Solving 800 + x = 969.535971483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-800' to each side of the equation. 800 + -800 + x = 969.535971483 + -800 Combine like terms: 800 + -800 = 0 0 + x = 969.535971483 + -800 x = 969.535971483 + -800 Combine like terms: 969.535971483 + -800 = 169.535971483 x = 169.535971483 Simplifying x = 169.535971483

Subproblem 2

x + 800 = -969.535971483 Simplifying x + 800 = -969.535971483 Reorder the terms: 800 + x = -969.535971483 Solving 800 + x = -969.535971483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-800' to each side of the equation. 800 + -800 + x = -969.535971483 + -800 Combine like terms: 800 + -800 = 0 0 + x = -969.535971483 + -800 x = -969.535971483 + -800 Combine like terms: -969.535971483 + -800 = -1769.535971483 x = -1769.535971483 Simplifying x = -1769.535971483

Solution

The solution to the problem is based on the solutions from the subproblems. x = {169.535971483, -1769.535971483}

See similar equations:

| -.8x+40-8x-35= | | -4X-6+8X=24 | | 3.35+2x=4.25 | | 5ln(x-9)=1 | | -0.01x^2+20x=4x+3000 | | 2x+6x+7x=63 | | p=2d | | 5lnx-9=1 | | 5onx-9=1 | | 150x^4-216x^2=0 | | -4x+3+-2=-18 | | 7x-3x+4=x-16 | | 2/18d-15=12 | | 16-3x=0.67x+5 | | 4b+5-2b-1=12 | | -4a+-2a=12-6a | | 251-124=y | | 2(-4)=6x+8 | | 5.6a-4.6a+9.6=-5.1+4.1 | | 14x+7.9=0.6x | | 127+q=250 | | 4+4x=10-2x | | lne^5x+3=22 | | 8x+6.7=5x | | 5x^2-55x-60=0 | | p+128=287 | | n^2+n-1804289383=0 | | 5n^2+n-4=0 | | 101+r=295 | | 1+3-7a= | | 3b-6+b=22 | | 10x-2y=50 |

Equations solver categories