What are the solutions to the equation x^4-1/4-18750x^2=0 ?

The solutions to the equation x^4-1/4-18750x^2=0 are

Find the zeros of x^4-1/4-18750x^2=0

The zeros of x^4-1/4-18750x^2=0 are

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x^{4} - \frac{1}{4} - 18750 x^{2} = 0

x = \frac{75000 + 7500 0 ^{2} + 16}{2 2}, x = - \frac{75000 + 7500 0 ^{2} + 16}{2 2}, x = \frac{75000 - 7500 0 ^{2} + 16}{8}, x = - \frac{75000 - 7500 0 ^{2} + 16}{8}

Solution steps

x^{4} - \frac{1}{4} - 18750 x^{2} = 0

Multiply both sides by

4

4 x^{4} - 75000 x^{2} - 1 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

4 u^{2} - 75000 u - 1 = 0

Solve

4 u^{2} - 75000 u - 1 = 0 : u = \frac{75000 + 7500 0 ^{2} + 16}{8}, u = \frac{75000 - 7500 0 ^{2} + 16}{8}

u = \frac{75000 + 7500 0 ^{2} + 16}{8}, u = \frac{75000 - 7500 0 ^{2} + 16}{8}

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = \frac{75000 + 7500 0 ^{2} + 16}{8} : x = \frac{75000 + 7500 0 ^{2} + 16}{2 2}, x = - \frac{75000 + 7500 0 ^{2} + 16}{2 2}

Solve

x^{2} = \frac{75000 - 7500 0 ^{2} + 16}{8} : x = \frac{75000 - 7500 0 ^{2} + 16}{8}, x = - \frac{75000 - 7500 0 ^{2} + 16}{8}

The solutions are

x = \frac{75000 + 7500 0 ^{2} + 16}{2 2}, x = - \frac{75000 + 7500 0 ^{2} + 16}{2 2}, x = \frac{75000 - 7500 0 ^{2} + 16}{8}, x = - \frac{75000 - 7500 0 ^{2} + 16}{8}

z^{3} = 4

z^{3} = 0

\frac{x ^{3}}{i} - 27 = 0

x^{2} (5 x - 7) (3 x + 2) = 0

3 x^{3} + 4 x^{2} = 15 x

What are the solutions to the equation x^4-1/4-18750x^2=0 ?
The solutions to the equation x^4-1/4-18750x^2=0 are
Find the zeros of x^4-1/4-18750x^2=0
The zeros of x^4-1/4-18750x^2=0 are