1.5b(b+6)+9=24

Simple and best practice solution for 1.5b(b+6)+9=24 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 1.5b(b+6)+9=24 equation:


Simplifying
1.5b(b + 6) + 9 = 24

Reorder the terms:
1.5b(6 + b) + 9 = 24
(6 * 1.5b + b * 1.5b) + 9 = 24
(9b + 1.5b2) + 9 = 24

Reorder the terms:
9 + 9b + 1.5b2 = 24

Solving
9 + 9b + 1.5b2 = 24

Solving for variable 'b'.

Reorder the terms:
9 + -24 + 9b + 1.5b2 = 24 + -24

Combine like terms: 9 + -24 = -15
-15 + 9b + 1.5b2 = 24 + -24

Combine like terms: 24 + -24 = 0
-15 + 9b + 1.5b2 = 0

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

Divide each side by '1.5'.
-10 + 6b + b2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 6b + 10 + b2 = 0 + 10

Reorder the terms:
-10 + 10 + 6b + b2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 6b + b2 = 0 + 10
6b + b2 = 0 + 10

Combine like terms: 0 + 10 = 10
6b + b2 = 10

The b term is 6b.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6b + 9 + b2 = 10 + 9

Reorder the terms:
9 + 6b + b2 = 10 + 9

Combine like terms: 10 + 9 = 19
9 + 6b + b2 = 19

Factor a perfect square on the left side:
(b + 3)(b + 3) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(b + 3) equal to 4.358898944 and -4.358898944.

Subproblem 1

b + 3 = 4.358898944 Simplifying b + 3 = 4.358898944 Reorder the terms: 3 + b = 4.358898944 Solving 3 + b = 4.358898944 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = 4.358898944 + -3 Combine like terms: 3 + -3 = 0 0 + b = 4.358898944 + -3 b = 4.358898944 + -3 Combine like terms: 4.358898944 + -3 = 1.358898944 b = 1.358898944 Simplifying b = 1.358898944

Subproblem 2

b + 3 = -4.358898944 Simplifying b + 3 = -4.358898944 Reorder the terms: 3 + b = -4.358898944 Solving 3 + b = -4.358898944 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = -4.358898944 + -3 Combine like terms: 3 + -3 = 0 0 + b = -4.358898944 + -3 b = -4.358898944 + -3 Combine like terms: -4.358898944 + -3 = -7.358898944 b = -7.358898944 Simplifying b = -7.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. b = {1.358898944, -7.358898944}

See similar equations:

| 12a^2+12ab+3b^2=0 | | x^2+66x=0 | | 13x-2=11x+2x+10 | | -2=-5+z | | 12(4.99)+18x=30(8.98) | | 1.5b(b+x)+9=24 | | 96+184n+28n^2=0 | | 5-6(10-10p)=5(1+12p)+10p | | 7.5+x=4.5+4z | | 2236000-17740x=1985 | | -5(4p+4)-24=2(5p+8) | | 6y+10=8-(y+14) | | -6+14=12-8x | | 19m=9 | | 8-0.03x=1.72x+2.75 | | 4X+2X+2=3X-7 | | 10+4y=-18 | | Y+(-10)=-3 | | 5y-8=3+12 | | 4y+16=2y-4 | | 3x+5y=57 | | 2v^2(2v+3)= | | x^3-14x^2+8x+2=0 | | -17=17(w-4) | | -15+b-3=-9 | | (13b-1)-6(2b+1)=-5 | | -6x^3-28x^2-2x+140=0 | | -6x^3-28x^2-2z+140=0 | | 9y^2-15y=y+9 | | -41+7y+9=2(5y-4)-6 | | 80+43=12+18 | | 3(y-2)+9=8+y-5 |

Equations solver categories