What are the solutions to the equation (x^2+2x)^2=2x^2+4x+3 ?

The solutions to the equation (x^2+2x)^2=2x^2+4x+3 are x=-1,x=-3,x=1

Find the zeros of (x^2+2x)^2=2x^2+4x+3

The zeros of (x^2+2x)^2=2x^2+4x+3 are x=-1,x=-3,x=1

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

x = - 1, x = - 3, x = 1

Solution steps

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

Expand

(x^{2} + 2 x)^{2} : x^{4} + 4 x^{3} + 4 x^{2}

x^{4} + 4 x^{3} + 4 x^{2} = 2 x^{2} + 4 x + 3

Move

3

to the left side

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

Move

4 x

to the left side

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

Move

2 x^{2}

to the left side

x^{4} + 4 x^{3} + 2 x^{2} - 4 x - 3 = 0

Factor

x^{4} + 4 x^{3} + 2 x^{2} - 4 x - 3 : (x + 1)^{2} (x + 3) (x - 1)

(x + 1)^{2} (x + 3) (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x + 3 = 0 or x - 1 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x + 3 = 0 : x = - 3

Solve

x - 1 = 0 : x = 1

The solutions are

x = - 1, x = - 3, x = 1

p^{3} - 144 p = 0

x^{3} - 9 x^{2} - 22 x = 0

x^{3} + 2 x^{2} - 7 x = - 4

(x + 2 i) (x - 2 i) (x - 5) = 0

5 x^{3} + 13 x^{2} - 56 x + 20 = 0

What are the solutions to the equation (x^2+2x)^2=2x^2+4x+3 ?
The solutions to the equation (x^2+2x)^2=2x^2+4x+3 are x=-1,x=-3,x=1
Find the zeros of (x^2+2x)^2=2x^2+4x+3
The zeros of (x^2+2x)^2=2x^2+4x+3 are x=-1,x=-3,x=1