SOLUTION: Hi, having difficulty with this question: Sqrt(X-14) + sqrt(X-5) = 3 Thanks

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Question 960522: Hi, having difficulty with this question:
Sqrt(X-14) + sqrt(X-5) = 3
Thanks
Found 3 solutions by MathLover1, josgarithmetic, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28x-14%29+%2B+sqrt%28x-5%29+=+3........square both sides

%28sqrt%28x-14%29+%2B+sqrt%28x-5%29%29%5E2+=+3%5E2

%28sqrt%28x-14%29%29%5E2%2B2sqrt%28x-14%29%2Asqrt%28x-5%29+%2B+sqrt%28x-5%29%5E2+=+9

x-14%2B2sqrt%28%28x-14%29%28x-5%29%29+%2B+x-5+=+9

2x-19%2B2sqrt%28%28x-14%29%28x-5%29%29++=+9

2sqrt%28%28x-14%29%28x-5%29%29++=+9%2B19-2x

2sqrt%28%28x-14%29%28x-5%29%29++=+28-2x.........simplify

2sqrt%28%28x-14%29%28x-5%29%29%2F2++=+28%2F2-2x%2F2

sqrt%28%28x-14%29%28x-5%29%29++=+14-x .......square both sides again

%28sqrt%28%28x-14%29%28x-5%29%29%29%5E2++=+%2814-x%29%5E2

%28x-14%29%28x-5%29++=+14%5E2-28x%2Bx%5E2

cross%28x%5E2%29-5x-14x%2B70++=+196-28x%2Bcross%28x%5E2%29

-19x%2B70++=+196-28x

-19x%2B28x++=+196-70

9x++=+126

x++=+126%2F9

x++=+14

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Sqrt(X-14) + sqrt(X-5) = 3
Sqrt%28X-14%29+%2B+sqrt%28X-5%29+=+3

METHOD:
Isolate a radical;
Square both sides;
simplify;
isolate the radical;
simplify;
solve for the variable.

Using x instead of X,
sqrt%28x-14%29=3-sqrt%28x-5%29
x-14=9-6sqrt%28x-5%29%2Bx-5
-14=9-5-6sqrt%28x-5%29
-14-9%2B5=-6sqrt%28x-5%29
-17=-6sqrt%28x-5%29
sqrt%28x-5%29=17%2F6
x-5=%2817%2F6%29%5E2
highlight%28x=5%2B%2817%2F6%29%5E2%29, and you can simplify further if needed.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Hi, having difficulty with this question:
Sqrt(X-14) + sqrt(X-5) = 3
Thanks
sqrt%28x+-+14%29+%2B+sqrt%28x+-+5%29+=+3

sqrt%28x+-+14%29+=+3+-+sqrt%28x+-+5%29 --------- Subtracting sqrt%28x+-+5%29

%28sqrt%28x+-+14%29%29%5E2+=+%283+-+sqrt%28x+-+5%29%29%5E2 ---- Squaring both sides

x+-+14+=+9+-+6sqrt%28x+-+5%29+%2B+x+-+5

x+-+14+=+x+%2B+9+-+5+-+6sqrt%28x+-+5%29

x+-+14+=+x+%2B+4+-+6sqrt%28x+-+5%29

x+-+x+-+14+-+4+=+-+6sqrt%28x+-+5%29

-+18+=+-+6sqrt%28x+-+5%29

%28-+18%29%2F%28-+6%29+=+sqrt%28x+-+5%29

3+=+sqrt%28x+-+5%29

9 = x - 5 ------ Squaring both sides  

9 + 5 = x________highlight_green%2814+=+x%29