.5x-.001x^2=30

Simple and best practice solution for .5x-.001x^2=30 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 .5x-.001x^2=30 equation:


Simplifying
0.5x + -0.001x2 = 30

Solving
0.5x + -0.001x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + 0.5x + -0.001x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 0.5x + -0.001x2 = 0

Begin completing the square.  Divide all terms by
-0.001 the coefficient of the squared term: 

Divide each side by '-0.001'.
30000 + -500x + x2 = 0

Move the constant term to the right:

Add '-30000' to each side of the equation.
30000 + -500x + -30000 + x2 = 0 + -30000

Reorder the terms:
30000 + -30000 + -500x + x2 = 0 + -30000

Combine like terms: 30000 + -30000 = 0
0 + -500x + x2 = 0 + -30000
-500x + x2 = 0 + -30000

Combine like terms: 0 + -30000 = -30000
-500x + x2 = -30000

The x term is -500x.  Take half its coefficient (-250).
Square it (62500) and add it to both sides.

Add '62500' to each side of the equation.
-500x + 62500 + x2 = -30000 + 62500

Reorder the terms:
62500 + -500x + x2 = -30000 + 62500

Combine like terms: -30000 + 62500 = 32500
62500 + -500x + x2 = 32500

Factor a perfect square on the left side:
(x + -250)(x + -250) = 32500

Calculate the square root of the right side: 180.277563773

Break this problem into two subproblems by setting 
(x + -250) equal to 180.277563773 and -180.277563773.

Subproblem 1

x + -250 = 180.277563773 Simplifying x + -250 = 180.277563773 Reorder the terms: -250 + x = 180.277563773 Solving -250 + x = 180.277563773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = 180.277563773 + 250 Combine like terms: -250 + 250 = 0 0 + x = 180.277563773 + 250 x = 180.277563773 + 250 Combine like terms: 180.277563773 + 250 = 430.277563773 x = 430.277563773 Simplifying x = 430.277563773

Subproblem 2

x + -250 = -180.277563773 Simplifying x + -250 = -180.277563773 Reorder the terms: -250 + x = -180.277563773 Solving -250 + x = -180.277563773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = -180.277563773 + 250 Combine like terms: -250 + 250 = 0 0 + x = -180.277563773 + 250 x = -180.277563773 + 250 Combine like terms: -180.277563773 + 250 = 69.722436227 x = 69.722436227 Simplifying x = 69.722436227

Solution

The solution to the problem is based on the solutions from the subproblems. x = {430.277563773, 69.722436227}

See similar equations:

| 3x-5x+4=12 | | 40=4w-16 | | 3z-8-2(z+5)=0 | | 7x+3=4x-5 | | 5x+10+13x-10=180 | | 2+6a=-8+8a | | 8x+4=4x | | 3+14x= | | 7m^2-51m-40=0 | | 7k^2-15k+2=0 | | 4(t-4)+3=t+1 | | 6-4x=3-4x | | 6(2-1)=-3 | | (4+4y)=12 | | 6(2-1)=3 | | 6b+5b=11 | | 9(4x-3)-5(4-3x)=-x-7 | | (5w^2-6w+4)(3w+7)= | | 100a^2-20a-224=0 | | -5v-5=1-8v | | 34+6x=9x-2 | | 5x+2(x-3)=15 | | 40r^2-64r-32=0 | | -4p+6=p-4p | | 8x-3=19-6x | | 7+6p=6p+7 | | 28x^2+9x-4=0 | | n-6.5=2.5 | | 5r^2+17r-12=0 | | 5x+2=2x+18 | | 4x-10=6x-20 | | k-19=32 |

Equations solver categories