Use the quadratic formula to solve the equation x2+7x

The solution of the equation x2+7x is 0, -7 using the quadratic formula.

Step-by-step explanation:

x2 + 7x = 0

-b  ± √ b2 - 4(ac)/ 2a

substitution,

a = 1, b = 7, c = 0

= -7  ± √(7)2 - 4(1 x 0) / 2 x 1

= - 7   ± 7 / 2

x = 0 , -7

For this problem, I will use diagram.
First if all, we know that Kate used 1 cup of lemon juice and 2 cups sugar, so we have this:
1 cup of lemon juice=2 cups sugar
Then, the problem asked to find how many cups of lemon juice does Kate needs with 10 cups of sugar, and now we have have the complete tree diagram

1 cup of lemon juice= 2 cups of sugar
?cups of lemon juice=10 cups of sugar
Step 1:
Use cross multiply
10×1=10
Step 2:
Use division
10÷2=5
As a result, Kate will need 5 cups of lemon juice with 10 cups sugar
But there is another way to find the answer, too. If you curious, here is the second way:
The ratio between cup of sugar/cup of lemon juice, so
2 cups of sugar/1 cup of lemon juice. In conclusion, Kate use double amount of sugar than lemon juice, so the question asked us to find how many cups of lemon juice does Kate needs with 10 cups sugar. To find the answer, take 10÷2=5 cups of lemon of juice is your final answer. Hope it help!