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

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

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

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

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

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

Decimal Notation

x = 2, x = - 0.5

Solution steps

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

Expand

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

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

Move

3

to the left side

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

Solve with the quadratic formula

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

(- 3)^{2} - 4 \cdot 2 (- 2) = 5

x_{1, 2} = \frac{- ( - 3 ) \pm 5}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 5}{2 \cdot 2}, x_{2} = \frac{- ( - 3 ) - 5}{2 \cdot 2}

x = \frac{- ( - 3 ) + 5}{2 \cdot 2} : 2

x = \frac{- ( - 3 ) - 5}{2 \cdot 2} : - \frac{1}{2}

The solutions to the quadratic equation are:

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

5 x^{2} + 48 x - 20 = 0

(3 x - 6)^{2} = 33

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

6 x + 7.2 + (- 9.9) x^{2} = 0

9 x^{2} + 15 x = 14

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