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

The answer to sqrt(2x+5)-3/(sqrt(2x+5))=-2 is x=-2

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

Solution

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

Solution

x = - 2

Solution steps

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

Multiply both sides by

2 x + 5

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

Simplify

(2 x + 5)^{2} - 3 = - 2 2 x + 5

Move

2 2 x + 5

to the left side

(2 x + 5)^{2} - 3 + 2 2 x + 5 = 0

Factor

(2 x + 5)^{2} - 3 + 2 2 x + 5 : (2 x + 5 - 1) (2 x + 5 + 3)

(2 x + 5 - 1) (2 x + 5 + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 x + 5 - 1 = 0 or 2 x + 5 + 3 = 0

Solve

2 x + 5 - 1 = 0 : x = - 2

Solve

2 x + 5 + 3 = 0 :

No Solution for

x \in R

x = - 2

Verify Solutions:

x = - 2

True

The solution is

x = - 2

Graph

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Frequently Asked Questions (FAQ)

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

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

Solution

Solution

Graph

Popular Examples

Frequently Asked Questions (FAQ)

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

Solve for x: sqrt(2x+5)-3/(sqrt(2x+5))=-2