Finding a Solution through Substitution

8.9.1 Finding a Solution through Substitution

8.9.1 • Finding a Solution through Substitution

Warm Up

Let's try to find at least one solution to $x^{2} - 2 x - 35 = 0$ .

Create a table of values. In column 1, enter the whole numbers between 0 and 10 to represent values of $x$ . In column 2, evaluate the expression $x^{2} - 2 x - 35$ using the values for $x$ .

Compare your answer:

$x$	0	1	2	3	4	5	6	7	8	9	10
$x^{2} - 2 x - 35$	–35	–36	–35	–32	–27	–20	–11	0	13	28	45

This table displays the values of x and the quadratic expression x^2 - 2x - 35 for integer values of x from 0 to 10.

We can see from the table that a solution to the equation is $x = 7$ since $x^{2} - 2 x - 35 = 0$ at that value.

There is another number outside of 0 to 10 that would make the expression $x^{2} - 2 x - 35$ equal 0. Can you find it?

Compare your answer:

The other zero for the equation is located at $x = - 5$ , but it is possible that you did not consider negative numbers.