Solve: x2 + 2x + 1 = 16.
We can factor the left-hand side of this equation to see that:
(x + 1)2 = 16
Then snag the square root of both sides:
x + 1 = ±4
Solve the two equations:
x + 1 = 4 and x + 1 = -4
And our solutions are x = 3 and x = -5. Phew. It's nice to have some closure on that.
Solve: x2 = 5.
The answers are , and there's no prettier way to write them. We could inscribe them inside a drawing of a floral wreath, but that's about it.
Solve (x – 6)2 = 15.
We take the square root to find:
So we need to solve these two equations:
The solutions are, respectively:
That's as nice as they get. Getting uglier. Must...look...away...
Solve -2x2 = 16.
We divide both sides by -2 to find x2 = -8.
Now we're stuck, without any butter or Vaseline handy. There is no real number whose square is -8. This equation has no real number solutions. Unreal.
Make it rain.
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