1000q-q^2=80

Simple and best practice solution for 1000q-q^2=80 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 1000q-q^2=80 equation:


Simplifying
1000q + -1q2 = 80

Solving
1000q + -1q2 = 80

Solving for variable 'q'.

Reorder the terms:
-80 + 1000q + -1q2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + 1000q + -1q2 = 0

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

Divide each side by '-1'.
80 + -1000q + q2 = 0

Move the constant term to the right:

Add '-80' to each side of the equation.
80 + -1000q + -80 + q2 = 0 + -80

Reorder the terms:
80 + -80 + -1000q + q2 = 0 + -80

Combine like terms: 80 + -80 = 0
0 + -1000q + q2 = 0 + -80
-1000q + q2 = 0 + -80

Combine like terms: 0 + -80 = -80
-1000q + q2 = -80

The q term is -1000q.  Take half its coefficient (-500).
Square it (250000) and add it to both sides.

Add '250000' to each side of the equation.
-1000q + 250000 + q2 = -80 + 250000

Reorder the terms:
250000 + -1000q + q2 = -80 + 250000

Combine like terms: -80 + 250000 = 249920
250000 + -1000q + q2 = 249920

Factor a perfect square on the left side:
(q + -500)(q + -500) = 249920

Calculate the square root of the right side: 499.919993599

Break this problem into two subproblems by setting 
(q + -500) equal to 499.919993599 and -499.919993599.

Subproblem 1

q + -500 = 499.919993599 Simplifying q + -500 = 499.919993599 Reorder the terms: -500 + q = 499.919993599 Solving -500 + q = 499.919993599 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + q = 499.919993599 + 500 Combine like terms: -500 + 500 = 0 0 + q = 499.919993599 + 500 q = 499.919993599 + 500 Combine like terms: 499.919993599 + 500 = 999.919993599 q = 999.919993599 Simplifying q = 999.919993599

Subproblem 2

q + -500 = -499.919993599 Simplifying q + -500 = -499.919993599 Reorder the terms: -500 + q = -499.919993599 Solving -500 + q = -499.919993599 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + q = -499.919993599 + 500 Combine like terms: -500 + 500 = 0 0 + q = -499.919993599 + 500 q = -499.919993599 + 500 Combine like terms: -499.919993599 + 500 = 0.080006401 q = 0.080006401 Simplifying q = 0.080006401

Solution

The solution to the problem is based on the solutions from the subproblems. q = {999.919993599, 0.080006401}

See similar equations:

| 5/(x-2)=15/27 | | Dm=x+2forx | | -4-2+2=2-6 | | 4b+4b-4=28 | | 7m^2=-140 | | -9/4y=27/4 | | 25x=-3+26x | | 7x+54=3x+26 | | (-8-5i)+(-3+6i)= | | -0.5x+2.1=6.4 | | -8t(2t-7)=0 | | 13x-43=9 | | 2x+3x-11=13 | | -9=12+11x | | 4x+17=3(2x+7) | | -6-5a^2=-106 | | 2=3[-4]-12 | | -13m+5m=14-38+24 | | 11s+2s+4s-15s-1=9 | | X^25-6x-18=0 | | 2p-12p=70 | | 3×x/2=6 | | 4x+5=2(3x-4)-2 | | 4x^4(2x+5)= | | (-7+6i)-(8+5i)= | | 15p-11p-3p=13 | | 2x+1-(-2-x)=2-(-x) | | 500x-x^2=80 | | 8c-4c=8 | | -16-3+25-37=-6-3m-6+4m | | 8(6x+5)=120 | | z+4z=20 |

Equations solver categories