√(x + 8) + √(x + 15) = √(9x + 40)

Kaycee Roche

Kaycee Roche

Answered question

2021-06-02

(x+8)+(x+15)(9x+40)

Answer & Explanation

Corben Pittman

Corben Pittman

Skilled2021-06-03Added 83 answers

(x+8)+(x+15)(9x+40)
x+8+2(x+8)(x+15)+x+15=9x+40
2(x+8)(x+15)=7x+17
4(x+8)(x+15)=49x2+238x+289
4x2+92x+480=49x2+238x+283
45x2+146x191=0
(45x+191)(x1)=0
x=(19145)orx=1
Note at this point that the couple of times we squared both sides could have introduced extraneous solutions. So we'll need to test each individually. x=1x=1 is easy to check and turns out to be a solution. For −191/45, I'd recommend putting it in WolframAlpha. Doing so, you should see that
((19145)+8)+((19145)+15)5.22
(9((19145))+40)1.34
So x=1 is the only solution.

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