What are the solutions to the equation 4x^4=65x^2-196 ?

The solutions to the equation 4x^4=65x^2-196 are x= 7/2 ,x=-7/2 ,x=2,x=-2

Find the zeros of 4x^4=65x^2-196

The zeros of 4x^4=65x^2-196 are x= 7/2 ,x=-7/2 ,x=2,x=-2

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4 x^{4} = 65 x^{2} - 196

x = \frac{7}{2}, x = - \frac{7}{2}, x = 2, x = - 2

Decimal Notation

x = 3.5, x = - 3.5, x = 2, x = - 2

Solution steps

4 x^{4} = 65 x^{2} - 196

Move

196

to the left side

4 x^{4} + 196 = 65 x^{2}

Move

65 x^{2}

to the left side

4 x^{4} + 196 - 65 x^{2} = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

4 x^{4} - 65 x^{2} + 196 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

4 u^{2} - 65 u + 196 = 0

Solve

4 u^{2} - 65 u + 196 = 0 : u = \frac{49}{4}, u = 4

u = \frac{49}{4}, u = 4

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = \frac{49}{4} : x = \frac{7}{2}, x = - \frac{7}{2}

Solve

x^{2} = 4 : x = 2, x = - 2

The solutions are

x = \frac{7}{2}, x = - \frac{7}{2}, x = 2, x = - 2

((5 x - 16)^{3} - 4)^{3} = 216000

3 x^{4} - 24 = 0

x^{4} + x^{3} + 10 x^{2} + 16 x - 96 = 0

2 x^{5} - x + 1 = 0

(3 x^{2} - 13 x + 14) (x^{2} - 4 x + 1) = 0

What are the solutions to the equation 4x^4=65x^2-196 ?
The solutions to the equation 4x^4=65x^2-196 are x= 7/2 ,x=-7/2 ,x=2,x=-2
Find the zeros of 4x^4=65x^2-196
The zeros of 4x^4=65x^2-196 are x= 7/2 ,x=-7/2 ,x=2,x=-2