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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 a^{2} + 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

a^{2} + 14a = 51

a^{2} + 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

a^{2} + 14a = 51

a^{2} + 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

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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 a

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

a

a

(a + 7)

a + 7 = ± 10

Since it is given that a > 0, we choose a + 7 = 10.

We can also use factoring. Factoring method

a

a

(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

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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