What are the solutions to the equation (x-1)^2-(x-1)=42 ?

The solutions to the equation (x-1)^2-(x-1)=42 are x=8,x=-5

Find the zeros of (x-1)^2-(x-1)=42

The zeros of (x-1)^2-(x-1)=42 are x=8,x=-5

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(x - 1)^{2} - (x - 1) = 42

x = 8, x = - 5

Solution steps

(x - 1)^{2} - (x - 1) = 42

Expand

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

x^{2} - 3 x + 2 = 42

Move

42

to the left side

x^{2} - 3 x - 40 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 1 \cdot ( - 40 )}{2 \cdot 1}

(- 3)^{2} - 4 \cdot 1 \cdot (- 40) = 13

x_{1, 2} = \frac{- ( - 3 ) \pm 13}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 13}{2 \cdot 1}, x_{2} = \frac{- ( - 3 ) - 13}{2 \cdot 1}

x = \frac{- ( - 3 ) + 13}{2 \cdot 1} : 8

x = \frac{- ( - 3 ) - 13}{2 \cdot 1} : - 5

The solutions to the quadratic equation are:

x = 8, x = - 5

x^{2} + 11 x - 17 = 0

5 x^{2} - 2 = - 9 x

y^{2} + 3 y = 2

(1 - x)^{2} = 9

12 x^{2} + 16 x - 3 = 0

What are the solutions to the equation (x-1)^2-(x-1)=42 ?
The solutions to the equation (x-1)^2-(x-1)=42 are x=8,x=-5
Find the zeros of (x-1)^2-(x-1)=42
The zeros of (x-1)^2-(x-1)=42 are x=8,x=-5