w^2+5w-96=0

Simple and best practice solution for w^2+5w-96=0 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 w^2+5w-96=0 equation: 


Simplifying
w2 + 5w + -96 = 0

Reorder the terms:
-96 + 5w + w2 = 0

Solving
-96 + 5w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + 5w + 96 + w2 = 0 + 96

Reorder the terms:
-96 + 96 + 5w + w2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + 5w + w2 = 0 + 96
5w + w2 = 0 + 96

Combine like terms: 0 + 96 = 96
5w + w2 = 96

The w term is 5w.  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.
5w + 6.25 + w2 = 96 + 6.25

Reorder the terms:
6.25 + 5w + w2 = 96 + 6.25

Combine like terms: 96 + 6.25 = 102.25
6.25 + 5w + w2 = 102.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(w + 2.5) equal to 10.111874208 and -10.111874208.


Subproblem 1
w + 2.5 = 10.111874208

Simplifying
w + 2.5 = 10.111874208

Reorder the terms:
2.5 + w = 10.111874208

Solving
2.5 + w = 10.111874208

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = 10.111874208 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = 10.111874208 + -2.5
w = 10.111874208 + -2.5

Combine like terms: 10.111874208 + -2.5 = 7.611874208
w = 7.611874208

Simplifying
w = 7.611874208


Subproblem 2
w + 2.5 = -10.111874208

Simplifying
w + 2.5 = -10.111874208

Reorder the terms:
2.5 + w = -10.111874208

Solving
2.5 + w = -10.111874208

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = -10.111874208 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = -10.111874208 + -2.5
w = -10.111874208 + -2.5

Combine like terms: -10.111874208 + -2.5 = -12.611874208
w = -12.611874208

Simplifying
w = -12.611874208


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.611874208, -12.611874208}

See similar equations:

| 12x-74=22 | | .5(4z+7)+1.7=.7(4z-4) | | 51+12x=159 | | 15+9x=x-3 | | 10*3y=2 | | -5x-3=-2x+9 | | (x-1)/6=(x-1)/5 | | 40x=30x+120 | | x-4/3-3=x-1/2 | | 9x-6=3x-2 | | 6x+36=9x | | 2x/3-5/13=37/39 | | 2.1/42=7/t | | 5*2-Z*5=5 | | r/6.5=0.2/1.3 | | r/6.5 | | -16k=-32 | | 75*x=25 | | 12/25=u/40 | | 3/r=39/65 | | 100*x=99 | | 15/35=s/7 | | 8.5/25=x/50 | | -34+5x=41 | | 4/32=8/k | | q/18=90/135 | | 8/50=4/f | | .3(x+2)=5(x-6) | | 3.5/7.2=k/57.6 | | 5x-2=82-9x | | 58+-2x=54 | | n-(-19)=6 |

Equations solver categories