SOLUTION: square root (y-2) - square root (5y+1) = -3 solve for y

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Question 348248: square root (y-2) - square root (5y+1) = -3
solve for y
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
*Note: first isolate of the square roots to one side of the equation:
sqrt%28y-2%29%2B3+=+sqrt%285y%2B1%29
.
To solve: SQUARE BOTH SIDES OF THE EQUATION
+%28y-2%29%2B+6%2Asqrt%28y-2%29%2B9+=+%285y%2B1%29
.
combine like terms:
6%2Asqrt%28y-2%29=+4y-6
3%2Asqrt%28y-2%29=+2y-3
.
SQUARE BOTH SIDE OF THIS EQUATION
9%2A%28y-2%29=+4y%5E2+-12y+%2B9
0=+4y%5E2+-21y+%2B27
.
Solve with the Quadratic Formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-21x%2B27+=+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=%28-21%29%5E2-4%2A4%2A27=9.

Discriminant d=9 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--21%2B-sqrt%28+9+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-21%29%2Bsqrt%28+9+%29%29%2F2%5C4+=+3
x%5B2%5D+=+%28-%28-21%29-sqrt%28+9+%29%29%2F2%5C4+=+2.25

Quadratic expression 4x%5E2%2B-21x%2B27 can be factored:
4x%5E2%2B-21x%2B27+=+4%28x-3%29%2A%28x-2.25%29
Again, the answer is: 3, 2.25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-21%2Ax%2B27+%29