What is the answer to sqrt(x)-sqrt(x-9)=sqrt(x+11)-5 ?

The answer to sqrt(x)-sqrt(x-9)=sqrt(x+11)-5 is x=25

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt(x)-sqrt(x-9)=sqrt(x+11)-5

x - x - 9 = x + 11 - 5

x = 25

Solution steps

x - x - 9 = x + 11 - 5

Remove square roots

400 x^{3} - 31600 x^{2} + 414000 x + 8910000 = 9 x^{4} - 276 x^{3} - 16634 x^{2} + 287500 x + 9765625

Switch sides

x^{2} + 20 x x + 11 + 10 x - 900 x + 11 + 3125 = 4 x^{2} - 36 x

Move

x^{2}

to the right side

20 x x + 11 + 10 x - 900 x + 11 + 3125 = 3 x^{2} - 36 x

Move

10 x

to the right side

20 x x + 11 - 900 x + 11 + 3125 = 3 x^{2} - 46 x

Move

3125

to the right side

20 x x + 11 - 900 x + 11 = 3 x^{2} - 46 x - 3125

Factor

20 x x + 11 - 900 x + 11 : 20 x + 11 (x - 45)

20 x + 11 (x - 45) = 3 x^{2} - 46 x - 3125

Solve

400 x^{3} - 31600 x^{2} + 414000 x + 8910000 = 9 x^{4} - 276 x^{3} - 16634 x^{2} + 287500 x + 9765625 : x = 25, x \approx 42.57657 \dots

x = 25, x \approx 42.57657 \dots

Verify Solutions:

x = 25

True

, x \approx 42.57657 \dots

False

The solution is

x = 25

2 x^{\frac{4}{3}} - 2 = 160

x^{\frac{3}{2}} - 8 x^{- \frac{3}{2}} = 7

x^{\frac{1}{2}} - 4 x^{\frac{1}{4}} = 0

\frac{2 x ^{2} + 4}{x ^{2} + 4} = 0

x + 4 - x - 4 = 2

What is the answer to sqrt(x)-sqrt(x-9)=sqrt(x+11)-5 ?
The answer to sqrt(x)-sqrt(x-9)=sqrt(x+11)-5 is x=25
Solve for x: sqrt(x)-sqrt(x-9)=sqrt(x+11)-5
The solution is x=25