# Solve for w 9w^2-62w=7 9w2-62w=7
Move 7 to the left side of the equation by subtracting it from both sides.
9w2-62w-7=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=9⋅-7=-63 and whose sum is b=-62.
Factor -62 out of -62w.
9w2-62w-7=0
Rewrite -62 as 1 plus -63
9w2+(1-63)w-7=0
Apply the distributive property.
9w2+1w-63w-7=0
Multiply w by 1.
9w2+w-63w-7=0
9w2+w-63w-7=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(9w2+w)-63w-7=0
Factor out the greatest common factor (GCF) from each group.
w(9w+1)-7(9w+1)=0
w(9w+1)-7(9w+1)=0
Factor the polynomial by factoring out the greatest common factor, 9w+1.
(9w+1)(w-7)=0
(9w+1)(w-7)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
9w+1=0
w-7=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
9w+1=0
Subtract 1 from both sides of the equation.
9w=-1
Divide each term by 9 and simplify.
Divide each term in 9w=-1 by 9.
9w9=-19
Cancel the common factor of 9.
Cancel the common factor.
9w9=-19
Divide w by 1.
w=-19
w=-19
Move the negative in front of the fraction.
w=-19
w=-19
w=-19
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
w-7=0
Add 7 to both sides of the equation.
w=7
w=7
The final solution is all the values that make (9w+1)(w-7)=0 true.
w=-19,7
The result can be shown in multiple forms.
Exact Form:
w=-19,7
Decimal Form:
w=-0.1‾,7
Solve for w 9w^2-62w=7

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