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### Section 2.5 : Quadratic Equations - Part I

For problems 1 – 15 solve the quadratic equation by factoring.

1. $${z^2} - 11z + 24 = 0$$
2. $${w^2} + 13w + 12 = 0$$
3. $${x^2} + 32 = 12x$$
4. $${y^2} = 6y + 27$$
5. $${u^2} - 4u - 20 = 3u + 24$$
6. $${z^2} - 36 = 0$$
7. $$144{x^2} - 25 = 0$$
8. $$7{x^2} + 19x = 6$$
9. $$4{y^2} + 15y + 6 = 4y$$
10. $$6{z^2} - 11z + 15 = 12z - 5$$
11. $$20{v^2} + 3v = 5{v^2} + 5v + 1$$
12. $${x^2} - 4x + 16 = 4x$$
13. $$9{y^2} + 17y + 20 = 4 - 7y$$
14. $$7{u^2} + 9u = 0$$
15. $$14x = 3{x^2}$$

For problems 16 – 18 use factoring to solve the equation.

1. $$3{v^3} - 19{v^2} - 14v = 0$$
2. $${y^6} + {y^5} = 20{y^4}$$
3. $${z^4} + 2{z^3} + {z^2} = 0$$

For problems 19 – 22 use factoring to solve the equation.

1. $$\displaystyle 1 + \frac{2}{{x - 2}} = \frac{{12 - x}}{{{x^2} + x - 6}}$$
2. $$\displaystyle \frac{{t + 1}}{{t + 2}} = \frac{{4\left( {t - 5} \right)}}{{{t^2} + 2t}} + \frac{4}{t}$$
3. $$\displaystyle \frac{{{w^2} - 1}}{{w + 6}} = \frac{{5 - 5w}}{{w + 6}} - w$$
4. $$\displaystyle \frac{{y - 2}}{{y - 9}} + \frac{{{y^2} - 19y + 34}}{{{y^2} - 10y + 9}} = \frac{{y - 3}}{{y - 1}}$$

For problems 23 – 31 use the Square Root Property to solve the equation.

1. $${v^2} - 144 = 0$$
2. $$81{x^2} - 25 = 0$$
3. $$4{t^2} + 1 = 0$$
4. $$7{y^2} - 3 = 0$$
5. $$14 + 2{x^2} = 0$$
6. $${\left( {3t - 8} \right)^2} - 16 = 0$$
7. $${\left( {u + 11} \right)^2} + 6 = 0$$
8. $$4{\left( {2x - 1} \right)^2} - 36 = 0$$
9. $${\left( {4 - z} \right)^2} - 121 = 0$$