What are the solutions to the equation (2x^2-5)^2=39+10(2x^2-5) ?

The solutions to the equation (2x^2-5)^2=39+10(2x^2-5) are x=3,x=-3,x=1,x=-1

Find the zeros of (2x^2-5)^2=39+10(2x^2-5)

The zeros of (2x^2-5)^2=39+10(2x^2-5) are x=3,x=-3,x=1,x=-1

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(2 x^{2} - 5)^{2} = 39 + 10 (2 x^{2} - 5)

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

Solution steps

(2 x^{2} - 5)^{2} = 39 + 10 (2 x^{2} - 5)

Expand

(2 x^{2} - 5)^{2} : 4 x^{4} - 20 x^{2} + 25

Expand

39 + 10 (2 x^{2} - 5) : 20 x^{2} - 11

4 x^{4} - 20 x^{2} + 25 = 20 x^{2} - 11

Move

11

to the left side

4 x^{4} - 20 x^{2} + 36 = 20 x^{2}

Move

20 x^{2}

to the left side

4 x^{4} - 40 x^{2} + 36 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

4 u^{2} - 40 u + 36 = 0

Solve

4 u^{2} - 40 u + 36 = 0 : u = 9, u = 1

u = 9, u = 1

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 9 : x = 3, x = - 3

Solve

x^{2} = 1 : x = 1, x = - 1

The solutions are

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

z^{5} = 32

z^{5} = 14

3 x^{4} - 2 x^{3} - 27245 + 69 x - 9 x^{2} = 348062 x + 2

m^{3} + 2 m^{2} - 5 m - 6 = 0

2 x^{5} + 36 = 2 x - 6

What are the solutions to the equation (2x^2-5)^2=39+10(2x^2-5) ?
The solutions to the equation (2x^2-5)^2=39+10(2x^2-5) are x=3,x=-3,x=1,x=-1
Find the zeros of (2x^2-5)^2=39+10(2x^2-5)
The zeros of (2x^2-5)^2=39+10(2x^2-5) are x=3,x=-3,x=1,x=-1