Answer: x = 3 and x = -3
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Explanation:
We could add 9 to both sides, and then apply the square root to both sides. Don't forget about the plus minus
x^2 - 9 = 0
x^2 = 9
x = sqrt(9) or x = -sqrt(9)
x = 3 or x = -3
To check these answers, you replace x with those values we found. I'll show you how to check x = 3
x^2 - 9 = 0
(3)^2 - 9 = 0
9 - 9 = 0
0 = 0
So that confirms x = 3. The confirmation for x = -3 is nearly the same. Keep in mind that (-3)^2 = (-3)(-3) = 9. You'll be squaring the negative as well.
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Another method you could do is to use the difference of squares rule
x^2 - 9 = 0
x^2 - 3^2 = 0
(x - 3)(x + 3) = 0
Now apply the zero product property. This effectively means you set each factor equal to zero and solve for x
x-3 = 0 or x+3 = 0
x = 3 or x = -3
We end up with the same solution set.
Yet another method you could use is the quadratic formula, but that may be overkill. It's still good practice to do.
Graphing is a visual way to find the answers. You'll graph y = x^2 - 9 and look to see where the curve crosses or touches the horizontal x axis.
