Jazmin D.

asked • 09/14/14# how do you solve equation by extracting square root? 2(x-5)^2=17

2(x-5)^2=17 How do I solve this using extraction of square roots? HELP!!

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## 3 Answers By Expert Tutors

Steps

1. 2(x-5)^2=17 divide by 2 on both sides of the equation.

2. (x-5)^2 = 17/2 Take the square root of both sides of the equation

3. (x-5) = (17/2)^(1/2) add 5 to both sides of the equation

4. x = (8.5) ^ (1/2) +5

5. x = 2.92 + 5

6. x = 8.92

The solution above is incorrect. (Sorry, Jerrett. I think you may have written something incorrectly or something) There are going to be two answers.

Steps

1. The only thing an exponent applies to is the number or variable directly next to it, or expressions in parentheses when the parentheses is directly next to it. So in your question, the exponent only applies to the (x-5). We can't extract roots unless the exponent is by itself, so we want to move whats next to it- which is the 2. The 2 is being multiplied to the (x-5) so we do the opposite operation which will remove the 2- divide. But what we do to one side of the equal sign, we have to do to the other side; so we have to divide 17 by 2 also.

2(x-5)^2 = 17

_______ __

2 2

2. This leaves us with:

(x-5)^2 = 8.5

3. Now for the extraction of square roots. Just like in step 1 when we did the opposite operation to remove the 2, we want to do the opposite operation to remove the exponent. The opposite of an exponent is its root. In this case, the opposite of a square is the square root- which we get using radicals. Remember, what we do to one side of the =, we have to do to the other.

√(x-5)^2 = √8.5

4. This gives us:

(x-5) = +/- 2.91547594742

(Note: All real numbers have two square roots, one positive and one negative.

E.g. √4 = +/- 2

2*2=4

-2*-2=4)

5. So we write down our two problems:

x-5=2.91547594742 (this is the positive one- no need to write the + sign)

x-5=-2.91547594742

6. Solve:

x-5=2.91547594742 --> x-5 (+5)=2.91547594742 (+5) ---> x= 7.91547594742

x-5=-2.91547594742 ---> x-5 (+5)=-2.91547594742 (+5) ---> x = 2.08452405258

7. You can round these two answers to whatever digits you want or are asked to do. I'll round to the to the ten thousandth place.

x= 7.91547594742 ---> 7.9155

x = 2.08452405258 ---> 2.0845

8. To check:

2(7.915-5)^2=17 ---> 2(2.9155)^2=17 --> 2(8.50014025)=17 ---> 17.0002805=17 ---> 17=17

(You have a few extra numbers in the 17.0002805 because we rounded the answer. When you round numbers, you sometimes lose a little accuracy/exactness)

2(2.0845-5)^2=17 -->2(-2.9155)^2=17 --> 2(8.50014025)=17 -->17.0002805=17 ---> 17=17

(Same explanation as above. If you want, you can check it with the original long versions of your answer. It will equal exactly 17.)

Phillip R.

For equations such as this, we write the answer in radical form for the exact reason you state that rounding off creates an inaccurate answer. You can see my answer that I posted about an hour before. Suggesting rounding to the ten thousandth place or any other estimate is not recommended.

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09/14/14

Lisa K.

tutor

Hi Phillip. I understand that and completely agree, but it also depends on what the assignment calls for. I went on the assumption that the answer should be solved and written as a decimal because of what I have seen many times in similar assignments. But at least she has both options to choose from. :)

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09/14/14

Phillip R. answered • 09/14/14

Tutor

New to Wyzant
Top Notch Math and Science Tutoring from Brown Univ Grad

2(x-5)

^{2}= 17(x-5)

^{2}= 17/2x-5 = ±√(17/2)

x = 5 ± √(17/2)

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Phillip R.

09/14/14