# M:N:SPR:3

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If and what is the value of

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**10**

There is more than one way to solve this problem. A student can apply standard techniques by rewriting the equation as and then factoring. Since the coefficient of is 14 and the constant term is factoring requires writing 51 as the product of two numbers that differ by 14. This is which gives the factorization The possible values of are and Since it is given that it must be true that Thus, the value of is

A student could also use the quadratic formula to find the possible values of

The possible values of are and Again, since it is given that it must be true that Thus, the value of is

There is another way to solve this problem that will reward the student who recognizes that adding 49 to both sides of the equation yields or rather which has a perfect square on each side. Since the solution is evident.

Students must solve a quadratic equation.