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## which is the solution set for the quadratic equation x^2-9=0

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which is the solution set for the quadratic equation x^2-9=0

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Mathematics
3 years
2021-09-05T06:28:20+00:00
2021-09-05T06:28:20+00:00 1 Answers
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## Answers ( )

Answer: x = 3 and x = -3===================================================

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.