What is the answer to (r-3)/(sqrt(r))=-sqrt(r) ?

The answer to (r-3)/(sqrt(r))=-sqrt(r) is r= 3/2

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(r-3)/(sqrt(r))=-sqrt(r)

\frac{r - 3}{r} = - r

r = \frac{3}{2}

Decimal Notation

r = 1.5

Solution steps

\frac{r - 3}{r} = - r

Multiply both sides by

r

\frac{r - 3}{r} r = - r r

Simplify

r - 3 = - (r)^{2}

Rewrite the equation with

r = u

u^{2} - 3 = - u^{2}

Solve

u^{2} - 3 = - u^{2} : u = \frac{3}{2}, u = - \frac{3}{2}

u = \frac{3}{2}, u = - \frac{3}{2}

Substitute back

u = r,

solve for

r

Solve

r = \frac{3}{2} : r = \frac{3}{2}

Solve

r = - \frac{3}{2} :

No Solution for

r \in R

r = \frac{3}{2}

Verify Solutions:

r = \frac{3}{2}

True

The solution is

r = \frac{3}{2}

x + 4 x = 6

5 x + 6 = 17

2 - 7 x = x + 6

x = 3 x + 10 - 4

2 x + 54 + 12 = 20

What is the answer to (r-3)/(sqrt(r))=-sqrt(r) ?
The answer to (r-3)/(sqrt(r))=-sqrt(r) is r= 3/2
Solve for r: (r-3)/(sqrt(r))=-sqrt(r)
The solution is r= 3/2