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# Algebra : Solving Equations and Word Problems

1. Solve by factoring:
x^2 - 9x = -8

2. Solve using the square root property:
2x^2 - 5 = 93

3. Solve using the square root property:
(x + 4)^2 = 81

4. Solve by completing the square:
x^2 + 6x + 2 = 0

5. Solve using the quadratic formula:
x^2 - 3x = -6x - 1

6. Solve using the quadratic formula:
x^2 - 10x - 1 = -10

7. Solve the equation.

y^2 - 13 y + 22 = 0

8. Write the equation x(x - 6) + 5 = 0 in quadratic form and then solve it by factoring.

9. Write the equation 6 x(x - 3) = - 12 in quadratic form and then solve it by factoring.

10. Choose from the following a quadratic equation with solutions of 9 and 6.

x^2 - 15x + 54 = 0

x^2 - 18x + 51 = 0

x^2 - 15x + 57 = 0

x^2 - 12x + 54 = 0

11. The height h (in feet) of an object that is dropped from the height of s feet is given by the formula h = s - 16t 2 , where t is the time the object has been falling. A 6 foot tall woman on a sidewalk looks directly overhead and sees a window washer drop a bottle from the 2 story. How long does she have to get out of the way? Round to the nearest tenth. (A story is 12 feet.) Choose the answer from the following:

12. Use the quadratic formula to solve the equation: x 2 - 3 x + 2 = 0.

13. Use the quadratic formula to solve the equation: 4x^2 - 30x = 1

14. The hypotenuse of a right triangle is 2.7 units long. The longer leg is 1.4 units longer than the shorter leg. Find the lengths of the sides of the triangle.

15. We have learned to solve quadratic equations using a variety of methods including completing the square and the quadratic formula. Give an example using either completing the square or the quadratic formula and explain each step as if you were teaching someone who had never used the method before.

#### Solution Summary

Equations and word problems are solved. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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