SOLUTION: 7-sqrt(x2 − 3x)=sqrt((x2 − 3x) + 5) Step 1: Assume that we can represent (x2-3x) by u. Step 2: Rewrite the equation with u. Step 3: Solve the reduced equation given

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 7-sqrt(x2 − 3x)=sqrt((x2 − 3x) + 5) Step 1: Assume that we can represent (x2-3x) by u. Step 2: Rewrite the equation with u. Step 3: Solve the reduced equation given       Log On


   

Question 472213: 7-sqrt(x2 − 3x)=sqrt((x2 − 3x) + 5)
Step 1: Assume that we can represent (x2-3x) by u.
Step 2: Rewrite the equation with u.
Step 3: Solve the reduced equation given in Step 2 and replace u with the expression given in Step 1.
Step 4: What are the solutions of the original equation?
**sqrt=square root
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
u = x%5E2+-+3x
7+-+sqrt%28u%29+=+sqrt%28u%2B5%29
Square both sides
49+-14sqrt%28u%29+%2B+u+=+u+%2B+5
Subtract u on both sides
49+-14sqrt%28u%29+=++5
Subtract 49 on both sides
-14sqrt%28u%29+=+-44
Divide by -14 on both sides
sqrt%28u%29+=+22%2F7
Square both sides
u+=+484%2F49+=+9.877
Replace u with equivalent expression
x%5E2+-+3x+=+9.877
Set equation equal to zero
x%5E2+-+3x+-+9.877+=+0
Use quadratic formula to solve for x: x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%283+%2B-+sqrt%289+-+4%28-9.877%29%29%29%2F2
x+=+%283+%2B-+sqrt%2848.51%29%29%2F2
x+=+%283+%2B-+6.965%29%2F2