SOLUTION: SQRT(x + 8) + SQRT(x + 15) = SQRT(9x + 40). This must be squared twice and I'm stuck.

Algebra ->  Radicals -> SOLUTION: SQRT(x + 8) + SQRT(x + 15) = SQRT(9x + 40). This must be squared twice and I'm stuck.       Log On


   



Question 974369: SQRT(x + 8) + SQRT(x + 15) = SQRT(9x + 40). This must be squared twice and I'm stuck.
Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
SQRT(x + 8) + SQRT(x + 15) = SQRT(9x + 40). This must be squared twice and I'm stuck.
Where are you stuck? Why don't you show what you've done so someone can see and tell you why and/or
where you're getting stuck? I got highlight_green%28x+=+1%29
SOLUTION BELOW:
sqrt%28x+%2B+8%29+%2B+sqrt%28x+%2B+15%29+=+sqrt%289x+%2B+40%29
%28sqrt%28x+%2B+8%29+%2B+sqrt%28x+%2B+15%29%29%5E2+=+%28sqrt%289x+%2B+40%29%29%5E2 ------ Squaring both sides
%28x+%2B+8%29+%2B+2+%2A+sqrt%28%28x+%2B+8%29%28x+%2B+15%29%29+%2B+x+%2B+15+=+9x+%2B+40
x+%2B+8+%2B+x+%2B+15+%2B+2+%2A+sqrt%28x%5E2+%2B+23x+%2B+120%29+=+9x+%2B+40
2x+%2B+23+%2B+2+%2A+sqrt%28x%5E2+%2B+23x+%2B+120%29+=+9x+%2B+40
2+%2A+sqrt%28x%5E2+%2B+23x+%2B+120%29+=+9x+%2B+40+-+2x+-+23
2+%2A+sqrt%28x%5E2+%2B+23x+%2B+120%29+=+7x+%2B+17
%282+%2A+sqrt%28x%5E2+%2B+23x+%2B+120%29%29%5E2+=+%287x+%2B+17%29%5E2 ------- Squaring both sides
4%28x%5E2+%2B+23x+%2B+120%29+=+49x%5E2+%2B+238x+%2B+289
4x%5E2+%2B+92x+%2B+480+=+49x%5E2+%2B+238x+%2B+289
49x%5E2+-+4x%5E2+%2B+238x+-+92x+%2B+289+-+480+=+0
45x%5E2+%2B+146x+-+191+=+0
45x%5E2+%2B+191x+-+45x+-+191+=+0
x%2845x+%2B+191%29+-+1%2845x+%2B+191%29+=+0
(x – 1)(45x + 191) = 0
highlight_green%28x+=+1%29 OR x = -+191%2F45 (ignore)