00:01
In this problem, we're given the equation x minus 3 squared equals negative 9, and we're asked to solve using the square root property.
00:10
And so our first step is to take the square root of both sides, which gives us x minus 3 equals plus or minus the square root of negative 9.
00:21
And there is no real solution to this equation, because there's no number that one squared results in a negative number.
00:29
But there are imaginary solutions, and so we need to work with imaginary numbers to solve it.
00:38
And so we're going to change this square root into an imaginary number by expressing it in terms of i.
00:48
And so the square root of negative 9 can be rewritten as the square root of 9 times negative 1, which can be written as the square root of 9 times the square root of negative 1.
01:05
And that gives us our imaginary unit i, and the square root of 9 is 3.
01:11
So the square root of negative 9 can be expressed as 3i.
01:16
And so we can rewrite the equation as x minus 3 equals plus or minus 3i.
01:25
And this implies that either x minus three equals three i positive three i or x minus three equals negative three i and to solve this equation we can add three to both sides and so either x equals three plus three i or x equals three minus three i and so our next step is to check each solution in the original equation to see which one is correct...