w^2+w-66=0

Simple and best practice solution for w^2+w-66=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-66=0 equation: 


Simplifying
w2 + w + -66 = 0

Reorder the terms:
-66 + w + w2 = 0

Solving
-66 + w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + w + 66 + w2 = 0 + 66

Reorder the terms:
-66 + 66 + w + w2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + w + w2 = 0 + 66
w + w2 = 0 + 66

Combine like terms: 0 + 66 = 66
w + w2 = 66

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 = 66 + 0.25

Reorder the terms:
0.25 + w + w2 = 66 + 0.25

Combine like terms: 66 + 0.25 = 66.25
0.25 + w + w2 = 66.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(w + 0.5) equal to 8.139410298 and -8.139410298.


Subproblem 1
w + 0.5 = 8.139410298

Simplifying
w + 0.5 = 8.139410298

Reorder the terms:
0.5 + w = 8.139410298

Solving
0.5 + w = 8.139410298

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 = 8.139410298 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 8.139410298 + -0.5
w = 8.139410298 + -0.5

Combine like terms: 8.139410298 + -0.5 = 7.639410298
w = 7.639410298

Simplifying
w = 7.639410298


Subproblem 2
w + 0.5 = -8.139410298

Simplifying
w + 0.5 = -8.139410298

Reorder the terms:
0.5 + w = -8.139410298

Solving
0.5 + w = -8.139410298

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 = -8.139410298 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -8.139410298 + -0.5
w = -8.139410298 + -0.5

Combine like terms: -8.139410298 + -0.5 = -8.639410298
w = -8.639410298

Simplifying
w = -8.639410298


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.639410298, -8.639410298}

See similar equations:

| 16+5y=9y | | 7b+3b+7+10=17 | | x^2+18x+81=-16 | | 12y-25=35 | | (17b-4)-4(4b+1)=-4 | | 1x=1x+2x+3 | | w/5-17=3 | | 7x=g+kx | | 7b+10=2b+20 | | (t+35)10=810 | | 11x+10x+7= | | 4x^2+8=152 | | 8x-9y=13 | | 4/9*T=10 | | v/6-2=1 | | 7q-93=887 | | .3x+.6=.9x-1.8 | | 4x=-16(-4)+4 | | 5x^2+13x=2x^2-4x+28 | | 2(x-1)-4=-6(x-7) | | r/26--406=423 | | 4x=-16(1)+4 | | 4x=-16(-8)+4 | | 15d-107=643 | | 1.2e+23= | | 3n+1halfn=42 | | 5(k-88)=25 | | s/7-2=1 | | 5(r-73)=95 | | 4x=-16(4)+4 | | f/6-1=3 | | 55x+y=176 |

Equations solver categories