What is the answer to (x-1)/(sqrt(x))=x-5/2 ?

The answer to (x-1)/(sqrt(x))=x-5/2 is x=4,x=(2-sqrt(3))/2

Solve for x: (x-1)/(sqrt(x))=x-5/2

The solution is x=4,x=(2-sqrt(3))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{x - 1}{x} = x - \frac{5}{2}

x = 4, x = \frac{2 - 3}{2}

Decimal Notation

x = 4, x = 0.13397 \dots

Solution steps

\frac{x - 1}{x} = x - \frac{5}{2}

Find Least Common Multiplier of

x, 2 : 2 x

Multiply by LCM=

2 x

\frac{x - 1}{x} \cdot 2 x = x \cdot 2 x - \frac{5}{2} \cdot 2 x

Simplify

2 (x - 1) = 2 x x - 5 x

Expand

2 (x - 1) : 2 x - 2

2 x - 2 = 2 x x - 5 x

Factor

2 x - 2 : 2 (x - 1)

Factor

2 x x - 5 x : x (2 x - 5)

2 (x - 1) = x (2 x - 5)

Square both sides:

4 x^{2} - 8 x + 4 = 4 x^{3} - 20 x^{2} + 25 x

4 x^{2} - 8 x + 4 = 4 x^{3} - 20 x^{2} + 25 x

Solve

4 x^{2} - 8 x + 4 = 4 x^{3} - 20 x^{2} + 25 x : x = 4, x = \frac{2 + 3}{2}, x = \frac{2 - 3}{2}

x = 4, x = \frac{2 + 3}{2}, x = \frac{2 - 3}{2}

Verify Solutions:

x = 4

True

, x = \frac{2 + 3}{2}

False

, x = \frac{2 - 3}{2}

True

The solutions are

x = 4, x = \frac{2 - 3}{2}

x + 18 + 16 = 19

- 12 = - x + 2 x + 24

x^{2} - 3 x + 2 + x^{3} - x - 6 = 0

30 - 3 x - 9 = 0

What is the answer to (x-1)/(sqrt(x))=x-5/2 ?
The answer to (x-1)/(sqrt(x))=x-5/2 is x=4,x=(2-sqrt(3))/2
Solve for x: (x-1)/(sqrt(x))=x-5/2
The solution is x=4,x=(2-sqrt(3))/2