What are the solutions to the equation (x-1)^2=7-x ?

The solutions to the equation (x-1)^2=7-x are x=3,x=-2

Find the zeros of (x-1)^2=7-x

The zeros of (x-1)^2=7-x are x=3,x=-2

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(x - 1)^{2} = 7 - x

x = 3, x = - 2

Solution steps

(x - 1)^{2} = 7 - x

Expand

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

x^{2} - 2 x + 1 = 7 - x

Move

x

to the left side

x^{2} - x + 1 = 7

Move

7

to the left side

x^{2} - x - 6 = 0

Solve with the quadratic formula

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

(- 1)^{2} - 4 \cdot 1 \cdot (- 6) = 5

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = 3, x = - 2

2 w^{2} + 3 w - 1 = 0

x^{2} - 0.9 x + 0.2 = 0

3 x^{2} = x - 5

x^{2} - 19 x + 6 = 0

(x - 2)^{2} - 49 = 0

What are the solutions to the equation (x-1)^2=7-x ?
The solutions to the equation (x-1)^2=7-x are x=3,x=-2
Find the zeros of (x-1)^2=7-x
The zeros of (x-1)^2=7-x are x=3,x=-2