9w2-62w=7

Move 7 to the left side of the equation by subtracting it from both sides.

9w2-62w-7=0

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.

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.

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