The equation is .

Rewrite the equation in standard form:

(Add 49 to each side)

               (Apply additive inverse property: )

Graph the related function:

Let .

.

Graph the related function .

Locate the x-intercepts of the graph. Notice that the vertex of the parabola is the only x-intercept. Therefore is only one solution, .

Check:

Solve by factoring:

In this trinomial, . You need to find two numbers with a sum of 7 and a product of  14. Make a list of the factors of 14 and look for the of factors with the sum of 7.

Apply the pattern: .

        (Substitute )

      (Apply distributive property: )

    (Apply distributive property: )

             (Apply distributive property: )

                 (Subtract 7 from each side)

                       (Apply additive inverse property: )

                             (Apply additive identity property: )

                               (Subtract: )

The equation is true.

The only one solution is .

The only one solution is .