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

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

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(a-3)/(sqrt(a))=-sqrt(a)

\frac{a - 3}{a} = - a

a = \frac{3}{2}

Decimal Notation

a = 1.5

Solution steps

\frac{a - 3}{a} = - a

Multiply both sides by

a

\frac{a - 3}{a} a = - a a

Simplify

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

Rewrite the equation with

a = 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 = a,

solve for

a

Solve

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

Solve

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

No Solution for

a \in R

a = \frac{3}{2}

Verify Solutions:

a = \frac{3}{2}

True

The solution is

a = \frac{3}{2}

x + x^{2} + 1^{2} = 2

12 x = 3 x

4 = z^{2} - 9

500 (1 + 0.4 (x - 1)^{0.75}) = 13000

40 = 4 x

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