What is the answer to (-x)/(sqrt(25-x^2))= 1/2 ?

The answer to (-x)/(sqrt(25-x^2))= 1/2 is x=-sqrt(5)

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(-x)/(sqrt(25-x^2))= 1/2

\frac{- x}{25 - x ^{2}} = \frac{1}{2}

x = - 5

Decimal Notation

x = - 2.23606 \dots

Solution steps

\frac{- x}{25 - x ^{2}} = \frac{1}{2}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

(- x) \cdot 2 = 25 - x^{2} \cdot 1

Expand

(- x) \cdot 2 : - 2 x

Expand

25 - x^{2} \cdot 1 : 25 - x^{2}

- 2 x = 25 - x^{2}

Square both sides:

4 x^{2} = 25 - x^{2}

4 x^{2} = 25 - x^{2}

Solve

4 x^{2} = 25 - x^{2} : x = 5, x = - 5

x = 5, x = - 5

Verify Solutions:

x = 5

False

, x = - 5

True

The solution is

x = - 5

x + 4 = 5 x + 4

y, x = y^{\frac{3}{2}}

x + x = 3 x + x^{2}

2 - x = 2 - 7 x

What is the answer to (-x)/(sqrt(25-x^2))= 1/2 ?
The answer to (-x)/(sqrt(25-x^2))= 1/2 is x=-sqrt(5)
Solve for x: (-x)/(sqrt(25-x^2))= 1/2
The solution is x=-sqrt(5)