w^2+w-85=0

Simple and best practice solution for w^2+w-85=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+w-85=0 equation: 


Simplifying
w2 + w + -85 = 0

Reorder the terms:
-85 + w + w2 = 0

Solving
-85 + w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + w + 85 + w2 = 0 + 85

Reorder the terms:
-85 + 85 + w + w2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + w + w2 = 0 + 85
w + w2 = 0 + 85

Combine like terms: 0 + 85 = 85
w + w2 = 85

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
w + 0.25 + w2 = 85 + 0.25

Reorder the terms:
0.25 + w + w2 = 85 + 0.25

Combine like terms: 85 + 0.25 = 85.25
0.25 + w + w2 = 85.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 85.25

Calculate the square root of the right side: 9.233092656

Break this problem into two subproblems by setting 
(w + 0.5) equal to 9.233092656 and -9.233092656.


Subproblem 1
w + 0.5 = 9.233092656

Simplifying
w + 0.5 = 9.233092656

Reorder the terms:
0.5 + w = 9.233092656

Solving
0.5 + w = 9.233092656

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = 9.233092656 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 9.233092656 + -0.5
w = 9.233092656 + -0.5

Combine like terms: 9.233092656 + -0.5 = 8.733092656
w = 8.733092656

Simplifying
w = 8.733092656


Subproblem 2
w + 0.5 = -9.233092656

Simplifying
w + 0.5 = -9.233092656

Reorder the terms:
0.5 + w = -9.233092656

Solving
0.5 + w = -9.233092656

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = -9.233092656 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -9.233092656 + -0.5
w = -9.233092656 + -0.5

Combine like terms: -9.233092656 + -0.5 = -9.733092656
w = -9.733092656

Simplifying
w = -9.733092656


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {8.733092656, -9.733092656}

See similar equations:

| 5+4v= | | 2s+10=s | | 0.3y=5.4+y | | 5n+4=3n+10 | | 3.7s=6 | | y=225-16t^2 | | r+(-12)=35 | | 136=-8(3n+4) | | 5+(-3)+2= | | 3x-2x-10=9 | | X^2-9X-52.75=0 | | -6r+(-4r)+8r=12 | | (x-10)(x-6)=32 | | -5z+2z=15 | | 12k-11k+5=20 | | (-5)+14+(-7)= | | 3u+(-19u)+17u=13 | | 8w-20w-(-8w)+-10=18 | | 2k-30=k+15+5+2 | | x*2+(x+1)*2=(2x-1)(x+3) | | 6d-4d=14 | | 7y-6y=14 | | -30k=-420 | | 234x^2+5=0 | | 6+(-5)+6= | | 17t-7t-8t=16 | | 5b-3+7=-18 | | 12n-5n-6n-1=17 | | 60-x=180 | | -2y+3x=4 | | -11q+9q=8 | | e^3lnx=0 |

Equations solver categories