What are the solutions to the equation x^4-25x^2=-100 ?

The solutions to the equation x^4-25x^2=-100 are x=2sqrt(5),x=-2sqrt(5),x=sqrt(5),x=-sqrt(5)

Find the zeros of x^4-25x^2=-100

The zeros of x^4-25x^2=-100 are x=2sqrt(5),x=-2sqrt(5),x=sqrt(5),x=-sqrt(5)

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x^{4} - 25 x^{2} = - 100

x = 25, x = - 25, x = 5, x = - 5

Decimal Notation

x = 4.47213 \dots, x = - 4.47213 \dots, x = 2.23606 \dots, x = - 2.23606 \dots

Solution steps

x^{4} - 25 x^{2} = - 100

Move

100

to the left side

x^{4} - 25 x^{2} + 100 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

u^{2} - 25 u + 100 = 0

Solve

u^{2} - 25 u + 100 = 0 : u = 20, u = 5

u = 20, u = 5

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 20 : x = 25, x = - 25

Solve

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

The solutions are

x = 25, x = - 25, x = 5, x = - 5

2 x^{3} + 8 x^{2} - 24 x = 0

x^{3} - 8 x^{2} + 9 x + 18 = 0

- 15 y^{4} = (D) (3 y^{2})

x^{6} + x^{3} - 42 = 0

6 y^{2} + 9 y = 15 y^{3}

What are the solutions to the equation x^4-25x^2=-100 ?
The solutions to the equation x^4-25x^2=-100 are x=2sqrt(5),x=-2sqrt(5),x=sqrt(5),x=-sqrt(5)
Find the zeros of x^4-25x^2=-100
The zeros of x^4-25x^2=-100 are x=2sqrt(5),x=-2sqrt(5),x=sqrt(5),x=-sqrt(5)