990Q-10Q^2=100

Simple and best practice solution for 990Q-10Q^2=100 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 990Q-10Q^2=100 equation: 


Simplifying
990Q + -10Q2 = 100

Solving
990Q + -10Q2 = 100

Solving for variable 'Q'.

Reorder the terms:
-100 + 990Q + -10Q2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 990Q + -10Q2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-10 + 99Q + -1Q2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-10 + 99Q + -1Q2)' equal to zero and attempt to solve:

Simplifying
-10 + 99Q + -1Q2 = 0

Solving
-10 + 99Q + -1Q2 = 0

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

Divide each side by '-1'.
10 + -99Q + Q2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -99Q + -10 + Q2 = 0 + -10

Reorder the terms:
10 + -10 + -99Q + Q2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -99Q + Q2 = 0 + -10
-99Q + Q2 = 0 + -10

Combine like terms: 0 + -10 = -10
-99Q + Q2 = -10

The Q term is -99Q.  Take half its coefficient (-49.5).
Square it (2450.25) and add it to both sides.

Add '2450.25' to each side of the equation.
-99Q + 2450.25 + Q2 = -10 + 2450.25

Reorder the terms:
2450.25 + -99Q + Q2 = -10 + 2450.25

Combine like terms: -10 + 2450.25 = 2440.25
2450.25 + -99Q + Q2 = 2440.25

Factor a perfect square on the left side:
(Q + -49.5)(Q + -49.5) = 2440.25

Calculate the square root of the right side: 49.398886627

Break this problem into two subproblems by setting 
(Q + -49.5) equal to 49.398886627 and -49.398886627.


Subproblem 1
Q + -49.5 = 49.398886627

Simplifying
Q + -49.5 = 49.398886627

Reorder the terms:
-49.5 + Q = 49.398886627

Solving
-49.5 + Q = 49.398886627

Solving for variable 'Q'.

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

Add '49.5' to each side of the equation.
-49.5 + 49.5 + Q = 49.398886627 + 49.5

Combine like terms: -49.5 + 49.5 = 0.0
0.0 + Q = 49.398886627 + 49.5
Q = 49.398886627 + 49.5

Combine like terms: 49.398886627 + 49.5 = 98.898886627
Q = 98.898886627

Simplifying
Q = 98.898886627


Subproblem 2
Q + -49.5 = -49.398886627

Simplifying
Q + -49.5 = -49.398886627

Reorder the terms:
-49.5 + Q = -49.398886627

Solving
-49.5 + Q = -49.398886627

Solving for variable 'Q'.

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

Add '49.5' to each side of the equation.
-49.5 + 49.5 + Q = -49.398886627 + 49.5

Combine like terms: -49.5 + 49.5 = 0.0
0.0 + Q = -49.398886627 + 49.5
Q = -49.398886627 + 49.5

Combine like terms: -49.398886627 + 49.5 = 0.101113373
Q = 0.101113373

Simplifying
Q = 0.101113373


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {98.898886627, 0.101113373}
Solution
Q = {98.898886627, 0.101113373}

See similar equations:

| 4x-2(5x^2-4x+4)+(8x^2+4x-2)= | | 2.4=c*15 | | 4(5x+5)=20x-1 | | c+b=56 | | -29v-9=28 | | 4(5x+5)=30x-1 | | xy-xy=35 | | 2(n+1)-(8-n)= | | -5m^2-4m-10-5m^2+4m+9= | | xy-yx=35 | | 3(1+6n)=8n-37 | | 2x+2y=68 | | 14(a-5)=-5-9 | | f(x)=0.75x+2 | | yx+bx= | | =8x^3-27y^3 | | h+22%=10 | | 6x-4x+3x= | | 3(8y-9)-(9y+3)= | | -2+22b=-24 | | 2x^2+2x+0=0 | | 300=0.5(9.8)x^2 | | 13y-1-12y+6=-10-5 | | y-16=-5 | | 20a^2=16-32a | | -16t^2+200t+5=0 | | 5(2x+3)=48 | | .75x^2=48 | | =2(l+b)m | | -3x-5-3=6 | | 28-6n=6(8-3n)-8 | | 2.27k-0.27k+0.6=11 |

Equations solver categories