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

The solutions to the equation ((x-2)(x-3))/6-((x-1)^2)/4 =2-x are x=3,x=5

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

The zeros of ((x-2)(x-3))/6-((x-1)^2)/4 =2-x are x=3,x=5

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

x = 3, x = 5

Solution steps

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

Find Least Common Multiplier of

6, 4 : 12

Multiply by LCM=

12

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

Simplify

2 (x - 2) (x - 3) - 3 (x - 1)^{2} = 24 - 12 x

Expand

2 (x - 2) (x - 3) - 3 (x - 1)^{2} : - x^{2} - 4 x + 9

- x^{2} - 4 x + 9 = 24 - 12 x

Move

12 x

to the left side

- x^{2} + 8 x + 9 = 24

Move

24

to the left side

- x^{2} + 8 x - 15 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 ( - 1 ) ( - 15 )}{2 ( - 1 )}

8^{2} - 4 (- 1) (- 15) = 2

x_{1, 2} = \frac{- 8 \pm 2}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 8 + 2}{2 ( - 1 )}, x_{2} = \frac{- 8 - 2}{2 ( - 1 )}

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

x = \frac{- 8 - 2}{2 ( - 1 )} : 5

The solutions to the quadratic equation are:

x = 3, x = 5

\frac{7}{10} \cdot \frac{6}{9}

6^{2} + x^{2} = 1 5^{2}

78 = 6 (- 6 a - 5)

\frac{7}{4} + \frac{2}{3}

- 18 > \frac{x}{6} - 10

What are the solutions to the equation ((x-2)(x-3))/6-((x-1)^2)/4 =2-x ?
The solutions to the equation ((x-2)(x-3))/6-((x-1)^2)/4 =2-x are x=3,x=5
Find the zeros of ((x-2)(x-3))/6-((x-1)^2)/4 =2-x
The zeros of ((x-2)(x-3))/6-((x-1)^2)/4 =2-x are x=3,x=5