# Solve for w (w-4)^2+4w^2-w=18 (w-4)2+4w2-w=18
Move 18 to the left side of the equation by subtracting it from both sides.
(w-4)2+4w2-w-18=0
Factor the left side of the equation.
Rewrite (w-4)2 as (w-4)(w-4).
(w-4)(w-4)+4w2-w-18=0
Expand (w-4)(w-4) using the FOIL Method.
Apply the distributive property.
w(w-4)-4(w-4)+4w2-w-18=0
Apply the distributive property.
w⋅w+w⋅-4-4(w-4)+4w2-w-18=0
Apply the distributive property.
w⋅w+w⋅-4-4w-4⋅-4+4w2-w-18=0
w⋅w+w⋅-4-4w-4⋅-4+4w2-w-18=0
Simplify and combine like terms.
Simplify each term.
Multiply w by w.
w2+w⋅-4-4w-4⋅-4+4w2-w-18=0
Move -4 to the left of w.
w2-4w-4w-4⋅-4+4w2-w-18=0
Multiply -4 by -4.
w2-4w-4w+16+4w2-w-18=0
w2-4w-4w+16+4w2-w-18=0
Subtract 4w from -4w.
w2-8w+16+4w2-w-18=0
w2-8w+16+4w2-w-18=0
Add w2 and 4w2.
5w2-8w+16-w-18=0
Subtract w from -8w.
5w2-9w+16-18=0
Subtract 18 from 16.
5w2-9w-2=0
Factor by grouping.
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=5⋅-2=-10 and whose sum is b=-9.
Factor -9 out of -9w.
5w2-9w-2=0
Rewrite -9 as 1 plus -10
5w2+(1-10)w-2=0
Apply the distributive property.
5w2+1w-10w-2=0
Multiply w by 1.
5w2+w-10w-2=0
5w2+w-10w-2=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(5w2+w)-10w-2=0
Factor out the greatest common factor (GCF) from each group.
w(5w+1)-2(5w+1)=0
w(5w+1)-2(5w+1)=0
Factor the polynomial by factoring out the greatest common factor, 5w+1.
(5w+1)(w-2)=0
(5w+1)(w-2)=0
(5w+1)(w-2)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
5w+1=0
w-2=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
5w+1=0
Subtract 1 from both sides of the equation.
5w=-1
Divide each term by 5 and simplify.
Divide each term in 5w=-1 by 5.
5w5=-15
Cancel the common factor of 5.
Cancel the common factor.
5w5=-15
Divide w by 1.
w=-15
w=-15
Move the negative in front of the fraction.
w=-15
w=-15
w=-15
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
w-2=0
Add 2 to both sides of the equation.
w=2
w=2
The final solution is all the values that make (5w+1)(w-2)=0 true.
w=-15,2
The result can be shown in multiple forms.
Exact Form:
w=-15,2
Decimal Form:
w=-0.2,2
Solve for w (w-4)^2+4w^2-w=18

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