What are the solutions to the equation (x-1)^2=2x+6 ?

The solutions to the equation (x-1)^2=2x+6 are x=5,x=-1

Find the zeros of (x-1)^2=2x+6

The zeros of (x-1)^2=2x+6 are x=5,x=-1

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(x - 1)^{2} = 2 x + 6

x = 5, x = - 1

Solution steps

(x - 1)^{2} = 2 x + 6

Expand

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

x^{2} - 2 x + 1 = 2 x + 6

Move

6

to the left side

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

Move

2 x

to the left side

x^{2} - 4 x - 5 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 \cdot 1 \cdot ( - 5 )}{2 \cdot 1}

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

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

Separate the solutions

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

x = \frac{- ( - 4 ) + 6}{2 \cdot 1} : 5

x = \frac{- ( - 4 ) - 6}{2 \cdot 1} : - 1

The solutions to the quadratic equation are:

x = 5, x = - 1

x^{2} + 2 x - 3

12 m^{2} - 5 m - 2 = 0

16 (1 - 2 x)^{2} - 6 = - 5

x^{2} = 2 (3 x - 4)

x^{2} + 3 x + 4

What are the solutions to the equation (x-1)^2=2x+6 ?
The solutions to the equation (x-1)^2=2x+6 are x=5,x=-1
Find the zeros of (x-1)^2=2x+6
The zeros of (x-1)^2=2x+6 are x=5,x=-1