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Week 2.2
——————Review Questions:
- Solving quadratic equations/Applications
- Completing the square
- And more
——————–
1. Solve 4x2 + 24x = 32 by completing the square. Check your solution by using the quadratic
equation.
2. Derive the quadratic equation by solving ax2 + bx = −c by completing the square, for real
numbers a, b, c.
3. A pool has dimension 10m by 20m. If the patio area around the pool has an area equal to the
pool, how wide is the patio?
4. Solve
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x6
+ x23 + 1 = 23
———————
New Material
- Solving square-root equations
- Absolute Values
———————
√
5. Solve 3 x=9.
6. Solve
√
3 − x = x.
7. Solve
√
√
5y + 1 − y + 1 = 2.
8. Solve
√
3 2
x + 6x − 2 = 0.
9. Solve |x| = 5.
10. Solve |x| = −5.
11. Solve |2x + 1| + 2 = 5.
12. Solve |2x + 3| + 6 = 5.
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13. Solve |x2 | = 4.
14. Solve |x2 + 4x + 4| = 4.
15. Solve |x2 + 4x| = 4.
16. Solve y3 + 2y2 = 81y + 162.
17. Complete the square for the following:
a) x2 + 16x
b) y2 + 9y
c) Using what you know from the above, write x2 + 4x + y2 + 9y = 0 so that it looks like (x + )2 +
(y + )2 = 2 .
18. You’re in a chemistry class, and you need to make 1 Litre of 10M Sulfuric Acid. (10 Moles of
H2 SO4 per Litre.) You only have 18M Sulfuric Acid, and 2M Sulfuric Acid. How much of each
solution do you need?
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