SOLUTION: Solve for x {{{sqrt(x-12) + sqrt(x+3) = 5}}} Solution is ----- Use commas to separate answers or Solution is not a real number Thank you so much for helping me grasp

Algebra ->  Radicals -> SOLUTION: Solve for x {{{sqrt(x-12) + sqrt(x+3) = 5}}} Solution is ----- Use commas to separate answers or Solution is not a real number Thank you so much for helping me grasp       Log On


   

Question 407972: Solve for x
sqrt%28x-12%29+%2B+sqrt%28x%2B3%29+=+5
Solution is ----- Use commas to separate answers or
Solution is not a real number

Thank you so much for helping me grasp this!!

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28x-12%29+%2B+sqrt%28x%2B3%29+=+5

Isolate one of the radical terms:

sqrt%28x-12%29+=+5+-+sqrt%28x%2B3%29

Square both sides:

%28sqrt%28x-12%29%29%5E2+=+%285+-+sqrt%28x%2B3%29%29%5E2

x-12++=+%285-sqrt%28x%2B3%29%29%285-sqrt%28x%2B3%29%29

x-12++=+25-5sqrt%28x%2B3%29-5sqrt%28x%2B3%29%2B%28sqrt%28x%2B3%29%29%5E2

x-12++=+25-10sqrt%28x%2B3%29%2Bx%2B3

x-12++=+28-10sqrt%28x%2B3%29%2Bx

Isolate the radical term:

10sqrt%28x%2B3%29=+40

Divide both sides by 10

sqrt%28x%2B3%29=+4

Square both sides:

%28sqrt%28x%2B3%29%29%5E2=4%5E2

x%2B3=16

x=13

You must always check a radical equation:

sqrt%28x-12%29+%2B+sqrt%28x%2B3%29+=+5

sqrt%2813-12%29+%2B+sqrt%2813%2B3%29+=+5

sqrt%281%29+%2B+sqrt%2816%29+=+5

1+%2B+4+=+5

5=5

It checks so the solution is x=13

Edwin