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

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

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

The zeros of x(x-3)=3(x-1)+2 are x=3+2sqrt(2),x=3-2sqrt(2)

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

x = 3 + 22, x = 3 - 22

Solution steps

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

Expand

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

Expand

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

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

Move

1

to the left side

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

Move

3 x

to the left side

x^{2} - 6 x + 1 = 0

Solve with the quadratic formula

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

(- 6)^{2} - 4 \cdot 1 \cdot 1 = 42

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

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 4 2}{2 \cdot 1}, x_{2} = \frac{- ( - 6 ) - 4 2}{2 \cdot 1}

x = \frac{- ( - 6 ) + 4 2}{2 \cdot 1} : 3 + 22

x = \frac{- ( - 6 ) - 4 2}{2 \cdot 1} : 3 - 22

The solutions to the quadratic equation are:

x = 3 + 22, x = 3 - 22

1 2^{x - 5} \geq 9.32

8 c^{3} + 343

4 x^{2} + 7 + 5 x + 8 = 3 x^{2} - 3 x

0.25 a + 0.5 = 4.5

3 d - 4 = 8

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