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By completing the square, solve for `b` given
`b^2-10b-125=0.` (3 marks)
`5+-5sqrt(6)`
| `b^2-10b-125` | `=0` |
| `b^2-10b+25-150` | `=0` |
| `(b-5)^2` | `=150` |
| `b-5` | `= +-sqrt(150)` |
| `b` | `=5+-sqrt(25xx6)` |
| `b` | `=5+-5sqrt(6)` |
By completing the square, solve for `x` given
`x^2-12x=-4.` (3 marks)
`6+-4sqrt(2)`
| `x^2-12x` | `=-4` |
| `x^2-12x+36` | `=-4+36` |
| `(x-6)^2` | `=32` |
| `x-6` | `= +-sqrt(32)` |
| `x` | `=6+-4sqrt(2)` |
By completing the square, solve for `y` given
`y^2-14y+37=0.` (3 marks)
`7+-2sqrt(3)`
| `y^2-14y+37` | `=0` |
| `y^2-14y+49-12` | `=0` |
| `(y-7)^2` | `=12` |
| `y-7` | `= +-sqrt(12)` |
| `y` | `=7+-2sqrt(3)` |
By completing the square, solve for `x` given
`x^2+4x-1 = 0.` (3 marks)
`-2+-sqrt(5)`
| `x^2+4x-1` | `=0` |
| `x^2+4x+4-5` | `=0` |
| `(x+2)^2` | `=5` |
| `x+2` | `= +-sqrt(5)` |
| `x` | `=-2+-sqrt(5)` |