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What do I do first in this problem? 4x(6x+6)=38

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2 Answers

4x(6x+6)=38

Step 1: Distribute 24x2 + 24x = 38

Step 2: Get rid of coefficient in front of x2, so factoring is easier.

                              x2 + x = 38/24

Step 3: Reduce the fraction on the right side.

                             x2 + x = 19/12

Step 4: Complete the square on the left side.

                            x2 + x + 1/4 = 19/12 + 1/4

Step 5: factor the equation on the left and reduce the numerical expression on the right.

                           (x + 1/2)2 = 22/12

Step 6: In order to solve for x, take the square root of the number on the right side. 

                          (x + 1/2) = (plus or minus) sqrt (22/12)

Step 7: x = 1/6 (-3 - sqrt(66))

            x = 1/6 (sqrt(66) - 3)

First you have to distribute the 6x to the 4x+4 to get.

24x^2+24x=38

Since there are no easy factors, we'll need to proceed with the completing square method.

First divide both sides by 24

x^2+x=38/24

Then complete the square on left

(x+1/2)^2 - 1/4 = 38/24

(x+1/2)^2 = 44/24

x+1/2 = +- 44/24

x = -1/2 +- 11/6

 

Comments

I noted that you have not take the sqrt of 44/24. Although all the steps are correct, this one error leads to an incorrect answer. I wrote an explanation that has corrected this error. All in all, the same steps are basically used for both our answers since this is the only way that one can solve the problem according the curriculum being taught.

You're correct.  I forgot to type out the sqrt().

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