Complete the equation to show two equivalent expressions. g2 – 4g – 21 = (g – )(g + )

Step-by-step explanation:

To complete the left side of the equation, we need to bring it to the form

expanding this expression we get:

Thus we have

from here we see that for both sides of the equation to be equal, it must be that

.

Getting rid of the negative signs we get:

At this point we can either guess the solution to this system (that's how you usually solve these types of problems) or solve for and systematically.

The solutions to this set are and . (you have to guess on this—it's easier)

Therefore, we have

which completes our equation

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3