# Basic Algebra Problems

10 algebra problems - work must be shown so I can understand how to compute.

Examples of questions:

--> Solve: x2 - 8x + 20 = 5

--> Solve by quadratic formula: -3x2 - 2x + 5 = 0

--> The crop yield in bushels for a field of tomatoes is 10x2 - 80x + 200 where x is number of pound of fertilizer used.

a) How many pounds of fertilizer should be used to maximize the yield?

b) What will be the maximum yield?

FOR COMPLETE LIST OF QUESTIONS PLEASE SEE ATTACHMENT

1. Solve x2 - 8x + 20 = 5

2. Solve

3. Solve and check for extraneous solutions

4. Solve by quadratic formula.

-3x2 - 2x + 5 = 0

5. Solve by quadratic formula.

-x2 - 3x + 5 = 0

6. The crop yield in bushels for a field of tomatoes is 10x2 - 80x + 200 where x is number of pound of fertilizer used.

a) How many pounds of fertilizer should be used to maximize the yield?

b) What will be the maximum yield?

7. Solve the inequality z2 - 16 < 0. State the interval(s) where the inequality is valid using the symbols <, >, <=, >= .

8. Solve the inequality . State the interval(s) where the inequality is valid using the symbols <, >, <=, >= .

9. Find all the real solutions to -2x2 - 7x - 4 = 0.

10. Find all the real solutions to 2x2 - 4x - 5 = 0

#### Solution Preview

Please see attached.

1. Solve x2 - 8x + 20 = 5

It is the same as

x2 - 8x + 20 -5 = 0, or x2 - 8x + 15 = 0

Factoring the left hand side, we have (x-5)(x-3)=0

So x=5 or x=3

2. Solve

Multiplying both sides by 3(x+1), we have x(x+1)=12, or x2 +x-12=0,

Factoring the left hand side, we have (x+4)(x-3)=0

So x=-4 or x=3

3. Solve and check for extraneous solutions

Squaring both sides, we have , or , so x=-3 or x=3.

But we want as it is a positive square root.

So the only solution is ...

#### Solution Summary

This solution is comprised of a detailed explanation to answer basic algebra problems.