What are the solutions to the equation 1/2 x 3/2 (x+1)-1/4 =5 ?

The solutions to the equation 1/2 x 3/2 (x+1)-1/4 =5 are x=(-1+sqrt(29))/2 ,x=-(1+sqrt(29))/2

Find the zeros of 1/2 x 3/2 (x+1)-1/4 =5

The zeros of 1/2 x 3/2 (x+1)-1/4 =5 are x=(-1+sqrt(29))/2 ,x=-(1+sqrt(29))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{1}{2} x \frac{3}{2} (x + 1) - \frac{1}{4} = 5

x = \frac{- 1 + 29}{2}, x = - \frac{1 + 29}{2}

Decimal Notation

x = 2.19258 \dots, x = - 3.19258 \dots

Solution steps

\frac{1}{2} x \frac{3}{2} (x + 1) - \frac{1}{4} = 5

Find Least Common Multiplier of

2, 4 : 4

Multiply by LCM=

4

\frac{1}{2} x \frac{3}{2} (x + 1) \cdot 4 - \frac{1}{4} \cdot 4 = 5 \cdot 4

Simplify

3 x (x + 1) - 1 = 20

Expand

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

3 x^{2} + 3 x - 1 = 20

Move

20

to the left side

3 x^{2} + 3 x - 21 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 \cdot 3 ( - 21 )}{2 \cdot 3}

3^{2} - 4 \cdot 3 (- 21) = 329

x_{1, 2} = \frac{- 3 \pm 3 29}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- 3 + 3 29}{2 \cdot 3}, x_{2} = \frac{- 3 - 3 29}{2 \cdot 3}

x = \frac{- 3 + 3 29}{2 \cdot 3} : \frac{- 1 + 29}{2}

x = \frac{- 3 - 3 29}{2 \cdot 3} : - \frac{1 + 29}{2}

The solutions to the quadratic equation are:

x = \frac{- 1 + 29}{2}, x = - \frac{1 + 29}{2}

9 z^{2} = 36

121 x^{2} - 4 = 0

2 x^{2} + 1 x = 0

1 + 2 x - x^{2} = 0

lo g_{10} (3) (x^{2}) + lo g_{10} (3) (x) - 6 = 0

What are the solutions to the equation 1/2 x 3/2 (x+1)-1/4 =5 ?
The solutions to the equation 1/2 x 3/2 (x+1)-1/4 =5 are x=(-1+sqrt(29))/2 ,x=-(1+sqrt(29))/2
Find the zeros of 1/2 x 3/2 (x+1)-1/4 =5
The zeros of 1/2 x 3/2 (x+1)-1/4 =5 are x=(-1+sqrt(29))/2 ,x=-(1+sqrt(29))/2