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Section 2.6 : Quadratic Equations - Part II

For problems 1 – 6 complete the square.

1. \({w^2} + 3w\)
2. \({x^2} - 10x\)
3. \({y^2} + 14y\)
4. \(3{u^2} - 36u\)
5. \(2{t^2} - 9t\)
6. \(18x - {x^2}\)

For problems 7 – 16 solve the quadratic equation by completing the square.

1. \({x^2} + 3x - 10 = 0\)
2. \({z^2} - 12z + 40 = 0\)
3. \({t^2} - 7t + 2 = 0\)
4. \({u^2} + 5u + 9 = 0\)
5. \(4{x^2} - 4x + 5 = 0\)
6. \(16{w^2} + 8w + 1 = 0\)
7. \(4{y^2} - 24y + 29 = 0\)
8. \(81{z^2} + 54z + 10 = 0\)
9. \(9{t^2} - 12t - 14 = 0\)
10. \(5{v^2} - 14v + 11 = 0\)

For problems 17 – 26 use the quadratic formula to solve the quadratic equation.

1. \({w^2} - 14w + 245 = 0\)
2. \(3{t^2} + 20t + 31 = 0\)
3. \(6x + 61 + 18{x^2} = 0\)
4. \({x^2} = 4x - 23\)
5. \({y^2} + 20y = 4y - 64\)
6. \(33 = 8z + {z^2}\)
7. \(2{t^2} + 49 = 32t - 2{t^2}\)
8. \(40u + 25{u^2} = 10u - 11\)
9. \(10{x^2} - 10x = 4{x^2} - 3x + 10\)
10. \(16{z^2} + 4z - 40 = 140z + 19\)