What are the solutions to the equation 3/2 (x/2-2)^2-(x+1)/8 = 1/8-(x-1)/4 ?

The solutions to the equation 3/2 (x/2-2)^2-(x+1)/8 = 1/8-(x-1)/4 are x=4,x= 11/3

Find the zeros of 3/2 (x/2-2)^2-(x+1)/8 = 1/8-(x-1)/4

The zeros of 3/2 (x/2-2)^2-(x+1)/8 = 1/8-(x-1)/4 are x=4,x= 11/3

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\frac{3}{2} (\frac{x}{2} - 2)^{2} - \frac{x + 1}{8} = \frac{1}{8} - \frac{x - 1}{4}

x = 4, x = \frac{11}{3}

Decimal Notation

x = 4, x = 3.66666 \dots

Solution steps

\frac{3}{2} (\frac{x}{2} - 2)^{2} - \frac{x + 1}{8} = \frac{1}{8} - \frac{x - 1}{4}

Find Least Common Multiplier of

2, 8, 4 : 8

Multiply by LCM=

8

\frac{3}{2} (\frac{x}{2} - 2)^{2} \cdot 8 - \frac{x + 1}{8} \cdot 8 = \frac{1}{8} \cdot 8 - \frac{x - 1}{4} \cdot 8

Simplify

12 (\frac{x}{2} - 2)^{2} - (x + 1) = 1 - 2 (x - 1)

Expand

12 (\frac{x}{2} - 2)^{2} - (x + 1) : 3 x^{2} - 25 x + 47

Expand

1 - 2 (x - 1) : - 2 x + 3

3 x^{2} - 25 x + 47 = - 2 x + 3

Move

3

to the left side

3 x^{2} - 25 x + 44 = - 2 x

Move

2 x

to the left side

3 x^{2} - 23 x + 44 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 23 ) \pm ( - 23 ) ^{2} - 4 \cdot 3 \cdot 44}{2 \cdot 3}

(- 23)^{2} - 4 \cdot 3 \cdot 44 = 1

x_{1, 2} = \frac{- ( - 23 ) \pm 1}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 23 ) + 1}{2 \cdot 3}, x_{2} = \frac{- ( - 23 ) - 1}{2 \cdot 3}

x = \frac{- ( - 23 ) + 1}{2 \cdot 3} : 4

x = \frac{- ( - 23 ) - 1}{2 \cdot 3} : \frac{11}{3}

The solutions to the quadratic equation are:

x = 4, x = \frac{11}{3}

y^{2} + 8 y + 15 = 0

8 x^{2} - 72 = 0

1 0^{2 x + 7} > 100 0^{x}

∣ 4 x - 3 ∣ = ∣ x + 14 ∣

25 x + 11 = - 6 x^{2}

What are the solutions to the equation 3/2 (x/2-2)^2-(x+1)/8 = 1/8-(x-1)/4 ?
The solutions to the equation 3/2 (x/2-2)^2-(x+1)/8 = 1/8-(x-1)/4 are x=4,x= 11/3
Find the zeros of 3/2 (x/2-2)^2-(x+1)/8 = 1/8-(x-1)/4
The zeros of 3/2 (x/2-2)^2-(x+1)/8 = 1/8-(x-1)/4 are x=4,x= 11/3