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

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

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

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

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

x = 1 + 2, x = 1 - 2

Decimal Notation

x = 2.41421 \dots, x = - 0.41421 \dots

Solution steps

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

Expand

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

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

Move

x

to the left side

2 x^{2} - 4 x - 2 = 0

Solve with the quadratic formula

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

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = 1 + 2, x = 1 - 2

75 x^{2} - 3 = 0

lo g_{5} (4) + lo g_{5} (5) x^{2} = 5

(4 x + 3)^{2} + 11 = - 17

x^{2} + 12 x + 46 = 0

- 4.9 x^{2} + 24.5 x + 2 = 0

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