SOLUTION: 6) Find all real solutions SR(x^2+3x+6) = 4 7) Perform the operation 6 + SR(-18) all divided by 3 thanks...i need help

Algebra ->  Radicals -> SOLUTION: 6) Find all real solutions SR(x^2+3x+6) = 4 7) Perform the operation 6 + SR(-18) all divided by 3 thanks...i need help       Log On


   

Question 179452: 6) Find all real solutions SR(x^2+3x+6) = 4

7) Perform the operation 6 + SR(-18) all divided by 3
thanks...i need help


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started

6)


sqrt%28x%5E2%2B3x%2B6%29+=+4+ Start with the given equation.


x%5E2%2B3x%2B6+=+4%5E2+ Square both sides.


x%5E2%2B3x%2B6+=+16+ Square 4 to get 16


x%5E2%2B3x%2B6-16=0 Subtract 16 from both sides.


x%5E2%2B3x-10=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=3, and c=-10


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%283%29+%2B-+sqrt%28+%283%29%5E2-4%281%29%28-10%29+%29%29%2F%282%281%29%29 Plug in a=1, b=3, and c=-10


x+=+%28-3+%2B-+sqrt%28+9-4%281%29%28-10%29+%29%29%2F%282%281%29%29 Square 3 to get 9.


x+=+%28-3+%2B-+sqrt%28+9--40+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-10%29 to get -40


x+=+%28-3+%2B-+sqrt%28+9%2B40+%29%29%2F%282%281%29%29 Rewrite sqrt%289--40%29 as sqrt%289%2B40%29


x+=+%28-3+%2B-+sqrt%28+49+%29%29%2F%282%281%29%29 Add 9 to 40 to get 49


x+=+%28-3+%2B-+sqrt%28+49+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-3+%2B-+7%29%2F%282%29 Take the square root of 49 to get 7.


x+=+%28-3+%2B+7%29%2F%282%29 or x+=+%28-3+-+7%29%2F%282%29 Break up the expression.


x+=+%284%29%2F%282%29 or x+=++%28-10%29%2F%282%29 Combine like terms.


x+=+2 or x+=+-5 Simplify.


So the answers are x+=+2 or x+=+-5