# Use the zero product property to find the solutions to the equation x^{2} - 9 = 16.

**Solution:**

In general, we say that zero of a polynomial p(x) is a number c such that p(c) = 0. The zero of the polynomial is obtained by equating it with zero. The value of x at which p(x) becomes zero becomes the root of the equation.

So by equating the given equation to zero we can find the solution. The standard form of quadratic equation is ax^{2} + bx + c = 0

By subtracting 16 from both the sides, we get

⇒ x^{2} – 9 - 16 = 0

⇒ x^{2} – 25 = 0

Using the equation x^{2} – 25 = 0 in algebraic identity a^{2} – b^{2}

⇒ x^{2} – 25 = 0

⇒ x^{2} – 5^{2} = 0

⇒ (x - 5) (x + 5) = 0

Now, we use the zero product property.

We can have two cases:

⇒ x - 5 = 0 or, x + 5 = 0

Hence, we have two solution: x = 5 and x = - 5.

## Use the zero product property to find the solutions to the equation x^{2 }- 9 = 16.

**Summary:**

Using the zero product property the solutions identified to the equation x^{2 }- 9 = 16 are x = 5 and x = -5.

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