90=10Q+2Q^2

Simple and best practice solution for 90=10Q+2Q^2 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 90=10Q+2Q^2 equation: 


Simplifying
90 = 10Q + 2Q2

Solving
90 = 10Q + 2Q2

Solving for variable 'Q'.

Reorder the terms:
90 + -10Q + -2Q2 = 10Q + -10Q + 2Q2 + -2Q2

Combine like terms: 10Q + -10Q = 0
90 + -10Q + -2Q2 = 0 + 2Q2 + -2Q2
90 + -10Q + -2Q2 = 2Q2 + -2Q2

Combine like terms: 2Q2 + -2Q2 = 0
90 + -10Q + -2Q2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(45 + -5Q + -1Q2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(45 + -5Q + -1Q2)' equal to zero and attempt to solve:

Simplifying
45 + -5Q + -1Q2 = 0

Solving
45 + -5Q + -1Q2 = 0

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

Divide each side by '-1'.
-45 + 5Q + Q2 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 5Q + 45 + Q2 = 0 + 45

Reorder the terms:
-45 + 45 + 5Q + Q2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 5Q + Q2 = 0 + 45
5Q + Q2 = 0 + 45

Combine like terms: 0 + 45 = 45
5Q + Q2 = 45

The Q term is 5Q.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5Q + 6.25 + Q2 = 45 + 6.25

Reorder the terms:
6.25 + 5Q + Q2 = 45 + 6.25

Combine like terms: 45 + 6.25 = 51.25
6.25 + 5Q + Q2 = 51.25

Factor a perfect square on the left side:
(Q + 2.5)(Q + 2.5) = 51.25

Calculate the square root of the right side: 7.158910532

Break this problem into two subproblems by setting 
(Q + 2.5) equal to 7.158910532 and -7.158910532.


Subproblem 1
Q + 2.5 = 7.158910532

Simplifying
Q + 2.5 = 7.158910532

Reorder the terms:
2.5 + Q = 7.158910532

Solving
2.5 + Q = 7.158910532

Solving for variable 'Q'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + Q = 7.158910532 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + Q = 7.158910532 + -2.5
Q = 7.158910532 + -2.5

Combine like terms: 7.158910532 + -2.5 = 4.658910532
Q = 4.658910532

Simplifying
Q = 4.658910532


Subproblem 2
Q + 2.5 = -7.158910532

Simplifying
Q + 2.5 = -7.158910532

Reorder the terms:
2.5 + Q = -7.158910532

Solving
2.5 + Q = -7.158910532

Solving for variable 'Q'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + Q = -7.158910532 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + Q = -7.158910532 + -2.5
Q = -7.158910532 + -2.5

Combine like terms: -7.158910532 + -2.5 = -9.658910532
Q = -9.658910532

Simplifying
Q = -9.658910532


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {4.658910532, -9.658910532}
Solution
Q = {4.658910532, -9.658910532}

See similar equations:

| d-155=5603 | | 4(2y+8)=5(3y-2) | | 83=8+2+7 | | s-909=4345 | | 8f-3=8f-5 | | 2x-7=97 | | -y^2-30=0 | | Cos8x=-1/2 | | 6(x+3)+2=2x-4 | | -3+7x+1= | | 7.99-5.19= | | 3(x-1)+5=0 | | m-2134=2251 | | 9u-28=-5(2-3u) | | 2.5x-2x=4 | | x^2+14x+27=0 | | 0.5(6x-8)=3x+5 | | 12n=8n-4(-5n-2) | | 6x+6=x-34 | | x^2+7x-392=0 | | x^2=(2)2x | | 87=3(7n+1) | | X+5+1-9x= | | x+139=989 | | V+20+12=51 | | 3(x^2+1)=1 | | 4x+2(-x-2)=-20 | | k-774/22=7 | | 2.2x=.66 | | y^2=4x-x | | 6a/{-2/5}= | | 3-3x+2+8x= |

Equations solver categories