 # Solving Quadratic Equations 5 - SAT

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This question is for the redesigned SAT, which is for you, if you are taking the SAT in March 2016 and beyond.

Calculator usage: No calculator
If a2 + 14a = 51 and a > 0, what is the value of a + 7?

There are a few ways to solve this problem.

The quickest way would be if you recognizes that adding 49 to both sides of the equation will get you a perfect square on both sides. Complete the Square method
a2 + 14a = 51
a2 + 14a + 49 = 51 + 49
(a + 7)2 = 100
a + 7 = ± 10
Since it is given that a > 0, we choose a + 7 = 10.

We can also use factoring. Factoring method
a2 + 14a = 51
a2 + 14a - 51 = 0
(a + 17)(a - 3)= 0
(You need to see that 3 and 17 are factors of 51 that differ by 14) a = -17 or a = 3
Since it is given that a > 0, we choose a = 3. The answer is a + 7 = 10.

We can also use the quadratic formula, but it will take the longest time to solve. Quadratic Formula

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