0.5(b^2+2b)=24

Simple and best practice solution for 0.5(b^2+2b)=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 0.5(b^2+2b)=24 equation:


Simplifying
0.5(b2 + 2b) = 24

Reorder the terms:
0.5(2b + b2) = 24
(2b * 0.5 + b2 * 0.5) = 24
(1b + 0.5b2) = 24

Solving
1b + 0.5b2 = 24

Solving for variable 'b'.

Reorder the terms:
-24 + 1b + 0.5b2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 1b + 0.5b2 = 0

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

Divide each side by '0.5'.
-48 + 2b + b2 = 0

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 2b + 48 + b2 = 0 + 48

Reorder the terms:
-48 + 48 + 2b + b2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 2b + b2 = 0 + 48
2b + b2 = 0 + 48

Combine like terms: 0 + 48 = 48
2b + b2 = 48

The b term is 2b.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2b + 1 + b2 = 48 + 1

Reorder the terms:
1 + 2b + b2 = 48 + 1

Combine like terms: 48 + 1 = 49
1 + 2b + b2 = 49

Factor a perfect square on the left side:
(b + 1)(b + 1) = 49

Calculate the square root of the right side: 7

Break this problem into two subproblems by setting 
(b + 1) equal to 7 and -7.

Subproblem 1

b + 1 = 7 Simplifying b + 1 = 7 Reorder the terms: 1 + b = 7 Solving 1 + b = 7 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = 7 + -1 Combine like terms: 1 + -1 = 0 0 + b = 7 + -1 b = 7 + -1 Combine like terms: 7 + -1 = 6 b = 6 Simplifying b = 6

Subproblem 2

b + 1 = -7 Simplifying b + 1 = -7 Reorder the terms: 1 + b = -7 Solving 1 + b = -7 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + b = -7 + -1 Combine like terms: 1 + -1 = 0 0 + b = -7 + -1 b = -7 + -1 Combine like terms: -7 + -1 = -8 b = -8 Simplifying b = -8

Solution

The solution to the problem is based on the solutions from the subproblems. b = {6, -8}

See similar equations:

| 13x+16y=624 | | (-35+25)(-7)+(3.14159265359)(16(-2))= | | 8(-6+8x)+5=(-1-8x)-9 | | 5/1.2 | | 3x+15x-18=0 | | v=abhfor | | 8/3=32/t | | -4y+9= | | 12/4=42/n | | 2x+2+3x-8=32 | | 267=25x+42 | | (-3)(z)=z+9.5 | | T/16=576/24 | | 10/8=n/12 | | (-5)(z)=z+9.5 | | 900n=3000*80+90 | | 5-8x/4 | | 15w-21=-221 | | 60/7-1=y | | 15*4=x | | 5x^2=1-2x | | 5-4x/2 | | (2x+9)+x=180 | | 1/3*4*9*1/2=x | | 32+5+8+15=x | | x^3-x^2+9x+27=0 | | 2x+10x-100= | | y=-2x^2-3x-6 | | ln(x+1)=6-x^2 | | -2c-2=3c+6 | | 3z-5=z+8 | | 2y*dx+(y^2-2*x)*dy=0 |

Equations solver categories