What is the answer to 2/(3+x)-sqrt(x+5)=0 ?

The answer to 2/(3+x)-sqrt(x+5)=0 is x\approx-1.86960…

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2/(3+x)-sqrt(x+5)=0

\frac{2}{3 + x} - x + 5 = 0

x \approx - 1.86960 \dots

Solution steps

\frac{2}{3 + x} - x + 5 = 0

Multiply both sides by

3 + x

\frac{2}{3 + x} (3 + x) - x + 5 (3 + x) = 0 \cdot (3 + x)

Simplify

2 - x + 5 (3 + x) = 0

Expand

2 - x + 5 (3 + x) : 2 - 3 x + 5 - x + 5 x

2 - 3 x + 5 - x + 5 x = 0

Move

2

to the right side

- 3 x + 5 - x + 5 x = - 2

Factor

- 3 x + 5 - x + 5 x : - x + 5 (3 + x)

- x + 5 (3 + x) = - 2

Square both sides:

x^{3} + 11 x^{2} + 39 x + 45 = 4

x^{3} + 11 x^{2} + 39 x + 45 = 4

Solve

x^{3} + 11 x^{2} + 39 x + 45 = 4 : x \approx - 1.86960 \dots

x \approx - 1.86960 \dots

Verify Solutions:

x \approx - 1.86960 \dots

True

The solution is

x \approx - 1.86960 \dots

y, x = 5 - y + 6

3 x + 1 + x + 8 = 5

3 x + 7 - x = 1

3 x + 7 - x = 3

x, x - 10 x + 9 = 0

What is the answer to 2/(3+x)-sqrt(x+5)=0 ?
The answer to 2/(3+x)-sqrt(x+5)=0 is x\approx-1.86960…
Solve for x: 2/(3+x)-sqrt(x+5)=0
The solution is x\approx-1.86960…