What are the solutions to the equation (x+1)/4-(x^2-2)/3 =(x^2-2)/6+1 ?

The solutions to the equation (x+1)/4-(x^2-2)/3 =(x^2-2)/6+1 are x=-1/2 ,x=1

Find the zeros of (x+1)/4-(x^2-2)/3 =(x^2-2)/6+1

The zeros of (x+1)/4-(x^2-2)/3 =(x^2-2)/6+1 are x=-1/2 ,x=1

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\frac{x + 1}{4} - \frac{x ^{2} - 2}{3} = \frac{x ^{2} - 2}{6} + 1

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

Decimal Notation

x = - 0.5, x = 1

Solution steps

\frac{x + 1}{4} - \frac{x ^{2} - 2}{3} = \frac{x ^{2} - 2}{6} + 1

Find Least Common Multiplier of

4, 3, 6 : 12

Multiply by LCM=

12

\frac{x + 1}{4} \cdot 12 - \frac{x ^{2} - 2}{3} \cdot 12 = \frac{x ^{2} - 2}{6} \cdot 12 + 1 \cdot 12

Simplify

3 (x + 1) - 4 (x^{2} - 2) = 2 (x^{2} - 2) + 12

Expand

3 (x + 1) - 4 (x^{2} - 2) : - 4 x^{2} + 3 x + 11

Expand

2 (x^{2} - 2) + 12 : 2 x^{2} + 8

- 4 x^{2} + 3 x + 11 = 2 x^{2} + 8

Move

8

to the left side

- 4 x^{2} + 3 x + 3 = 2 x^{2}

Move

2 x^{2}

to the left side

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

Solve with the quadratic formula

x_{1, 2} = \frac{- 3 \pm 3 ^{2} - 4 ( - 6 ) \cdot 3}{2 ( - 6 )}

3^{2} - 4 (- 6) \cdot 3 = 9

x_{1, 2} = \frac{- 3 \pm 9}{2 ( - 6 )}

Separate the solutions

x_{1} = \frac{- 3 + 9}{2 ( - 6 )}, x_{2} = \frac{- 3 - 9}{2 ( - 6 )}

x = \frac{- 3 + 9}{2 ( - 6 )} : - \frac{1}{2}

x = \frac{- 3 - 9}{2 ( - 6 )} : 1

The solutions to the quadratic equation are:

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

x^{2} - 14 x + 44 = 0

2 x^{2} = 338

2 x^{2} - 20 x + 50 = - 128

x, 150 = x^{2} + 2 x + 1

- (x - 2)^{2} + 4 = - 5

What are the solutions to the equation (x+1)/4-(x^2-2)/3 =(x^2-2)/6+1 ?
The solutions to the equation (x+1)/4-(x^2-2)/3 =(x^2-2)/6+1 are x=-1/2 ,x=1
Find the zeros of (x+1)/4-(x^2-2)/3 =(x^2-2)/6+1
The zeros of (x+1)/4-(x^2-2)/3 =(x^2-2)/6+1 are x=-1/2 ,x=1