SOLUTION: Im stuck on this problem. It says solve 12/√(5x+6)=√(2x+5) Thanks so much

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Question 155420This question is from textbook Introductory Algebra
: Im stuck on this problem.
It says solve
12/√(5x+6)=√(2x+5)
Thanks so muchThis question is from textbook Introductory Algebra

Found 2 solutions by Earlsdon, nerdybill:
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
12%2Fsqrt%285x%2B6%29+=+sqrt%282x%2B5%29 Multiply both sides bysqrt%285x%2B6%29
12+=+sqrt%282x%2B5%29%2Asqrt%285x%2B6%29Simplify the right side.
12+=+sqrt%28%282x%2B5%29%2A%285x%2B6%29%29 Now square both sides.
144+=+%282x%2B5%29%285x%2B6%29 Perform the indicated multiplication.
144+=+10x%5E2%2B37x%2B30 Subtract 144 from both sides.
10x%5E2%2B37x-114+=+0 Solve by the quadratic formula:x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a where: a = 10, b = 37, and c = -114.
x+=+%28-37%2B-sqrt%28%2837%29%5E2-4%2810%29%28-114%29%29%29%2F2%2810%29 Simplify.
x+=+%28-37%2B-sqrt%281369-%28-4560%29%29%29%2F20
x+=+%28-37%2B-sqrt%285929%29%29%2F20
x+=+%28-37%2B77%29%2F20 or x+=+%28-37-77%29%2F20
x+=+2 or x+=+-5.7

Answer by nerdybill(5404) About Me  (Show Source):
You can put this solution on YOUR website!
+12%2Fsqrt%285x%2B6%29+=+sqrt%282x%2B5%29+
.
To find 'x', start by multiplying both sides by +sqrt%285x%2B6%29+
+%2812%2Fsqrt%285x%2B6%29%29sqrt%285x%2B6%29+=+sqrt%282x%2B5%29sqrt%285x%2B6%29+
.
Notice the denominator cancels on the left. On the right we have:
+12+=+sqrt%28%282x%2B5%29%285x%2B6%29%29+
.
Now, we square both sides:
+144+=+%282x%2B5%29%285x%2B6%29+
.
Using FOIL, we expand the right side:
+144+=+10x%5E2+%2B+25x+%2B+12x+%2B+30+
+144+=+10x%5E2+%2B+37x+%2B+30+
+0+=+10x%5E2+%2B+37x+-+114+
.
Since, we can't factor, we must use the quadratic equation. Doing so, will produce two solutions:
x = {2, -5.7}
.
Reference: here is the quadratic solution
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 10x%5E2%2B37x%2B-114+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2837%29%5E2-4%2A10%2A-114=5929.

Discriminant d=5929 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-37%2B-sqrt%28+5929+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2837%29%2Bsqrt%28+5929+%29%29%2F2%5C10+=+2
x%5B2%5D+=+%28-%2837%29-sqrt%28+5929+%29%29%2F2%5C10+=+-5.7

Quadratic expression 10x%5E2%2B37x%2B-114 can be factored:
10x%5E2%2B37x%2B-114+=+10%28x-2%29%2A%28x--5.7%29
Again, the answer is: 2, -5.7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10%2Ax%5E2%2B37%2Ax%2B-114+%29