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.
Solve Quadratic Equation 5
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
More Lessons for Passport to Advanced Math
More Lessons for SAT Math
More Resources for SAT
Algebra Tutorials
This question is for the redesigned SAT, which is for you, if you are taking the SAT in March 2016 and beyond.
Solve Quadratic Equation 5
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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