2b(5-b)=9

Simple and best practice solution for 2b(5-b)=9 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 2b(5-b)=9 equation:


Simplifying
2b(5 + -1b) = 9
(5 * 2b + -1b * 2b) = 9
(10b + -2b2) = 9

Solving
10b + -2b2 = 9

Solving for variable 'b'.

Reorder the terms:
-9 + 10b + -2b2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 10b + -2b2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
4.5 + -5b + b2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -5b + -4.5 + b2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -5b + b2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -5b + b2 = 0 + -4.5
-5b + b2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-5b + b2 = -4.5

The b term is -5b.  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.
-5b + 6.25 + b2 = -4.5 + 6.25

Reorder the terms:
6.25 + -5b + b2 = -4.5 + 6.25

Combine like terms: -4.5 + 6.25 = 1.75
6.25 + -5b + b2 = 1.75

Factor a perfect square on the left side:
(b + -2.5)(b + -2.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(b + -2.5) equal to 1.322875656 and -1.322875656.

Subproblem 1

b + -2.5 = 1.322875656 Simplifying b + -2.5 = 1.322875656 Reorder the terms: -2.5 + b = 1.322875656 Solving -2.5 + b = 1.322875656 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = 1.322875656 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = 1.322875656 + 2.5 b = 1.322875656 + 2.5 Combine like terms: 1.322875656 + 2.5 = 3.822875656 b = 3.822875656 Simplifying b = 3.822875656

Subproblem 2

b + -2.5 = -1.322875656 Simplifying b + -2.5 = -1.322875656 Reorder the terms: -2.5 + b = -1.322875656 Solving -2.5 + b = -1.322875656 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + b = -1.322875656 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + b = -1.322875656 + 2.5 b = -1.322875656 + 2.5 Combine like terms: -1.322875656 + 2.5 = 1.177124344 b = 1.177124344 Simplifying b = 1.177124344

Solution

The solution to the problem is based on the solutions from the subproblems. b = {3.822875656, 1.177124344}

See similar equations:

| 3/5x+12=24 | | 9=m/-36 | | 17=d/17 | | 0.2*700= | | c/-2=-91 | | b(2b+1)=0 | | 2/3(5x-4)=1 | | 1-m/5=23 | | -7=q/11 | | 16=p/6 | | y/-3=8 | | (2b-11)(2b+11)=0 | | 2(a-1)+17=-6(a+6)+3 | | (2b+3)(2b+3)=0 | | 4.5*2.6= | | -8=b/8 | | y/2=13 | | 9x^2-19x+2=0 | | -60=-5a | | 9-6a=45 | | 2x^2-3=O | | 0=60t-16t^2+2 | | 5(7X+6)=90 | | 58=60t-16t^2+2 | | 28=q+28 | | 90=5X(7X+6) | | 16x^3-20x^2+20x-25=0 | | 11r-25=-3(r-1) | | 26=p-61 | | n-4=-11 | | -7=y+13 | | 4(3x-3)=2(6x+9) |

Equations solver categories