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

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

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

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

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

x = 2, x = - 1

Solution steps

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

Expand

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

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

Move

x

to the left side

x^{2} - x + 1 = 3

Move

3

to the left side

x^{2} - x - 2 = 0

Solve with the quadratic formula

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

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = 2, x = - 1

x^{2} - \frac{3}{2} x - 10 = 0

3 x^{2} - 5 x + 30 = 0

x = 2 x - x^{2}

2 x^{2} - 8 x + 12

2 x^{2} - 8 x + 17

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