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

The solutions to the equation x-7=(x-1)^2 are x= 3/2+i(sqrt(23))/2 ,x= 3/2-i(sqrt(23))/2

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

The zeros of x-7=(x-1)^2 are x= 3/2+i(sqrt(23))/2 ,x= 3/2-i(sqrt(23))/2

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

x = \frac{3}{2} + i \frac{23}{2}, x = \frac{3}{2} - i \frac{23}{2}

Solution steps

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

Expand

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

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

Switch sides

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

Move

7

to the left side

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

Move

x

to the left side

x^{2} - 3 x + 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 1 \cdot 8}{2 \cdot 1}

Simplify

(- 3)^{2} - 4 \cdot 1 \cdot 8 : 23 i

x_{1, 2} = \frac{- ( - 3 ) \pm 23 i}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 23 i}{2 \cdot 1}, x_{2} = \frac{- ( - 3 ) - 23 i}{2 \cdot 1}

x = \frac{- ( - 3 ) + 23 i}{2 \cdot 1} : \frac{3}{2} + i \frac{23}{2}

x = \frac{- ( - 3 ) - 23 i}{2 \cdot 1} : \frac{3}{2} - i \frac{23}{2}

The solutions to the quadratic equation are:

x = \frac{3}{2} + i \frac{23}{2}, x = \frac{3}{2} - i \frac{23}{2}

x, 25 x^{2} + k x + 4 = 0

4 x^{2} + 20 = 10 x + 3 x^{2} - 4

3 q^{2} - 147 = 0

2 x^{2} - 6 x + 5 = 0

(x + 3)^{2} - 169 = 0

What are the solutions to the equation x-7=(x-1)^2 ?
The solutions to the equation x-7=(x-1)^2 are x= 3/2+i(sqrt(23))/2 ,x= 3/2-i(sqrt(23))/2
Find the zeros of x-7=(x-1)^2
The zeros of x-7=(x-1)^2 are x= 3/2+i(sqrt(23))/2 ,x= 3/2-i(sqrt(23))/2