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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. \({\left( {4 - z} \right)^2} - 121 = 0\)