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

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

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

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

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

x = 3 - 22, x = 3 + 22

Decimal Notation

x = 0.17157 \dots, x = 5.82842 \dots

Solution steps

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

Expand

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

Expand

2 (x - 1)^{2} : 2 x^{2} - 4 x + 2

x^{2} + 2 x + 1 = 2 x^{2} - 4 x + 2

Move

2

to the left side

x^{2} + 2 x - 1 = 2 x^{2} - 4 x

Move

4 x

to the left side

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

Move

2 x^{2}

to the left side

- x^{2} + 6 x - 1 = 0

Solve with the quadratic formula

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

6^{2} - 4 (- 1) (- 1) = 42

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

Separate the solutions

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

x = \frac{- 6 + 4 2}{2 ( - 1 )} : 3 - 22

x = \frac{- 6 - 4 2}{2 ( - 1 )} : 3 + 22

The solutions to the quadratic equation are:

x = 3 - 22, x = 3 + 22

\frac{x}{3} = \frac{5 x - 9}{4} - \frac{x - 1}{2}

2 k^{2} + k - 10

4^{- 6}

9 - 4 (2 p - 1) = 41

x^{2} + 8 x + 65 = 0

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