Solve 4x^2-480x^625

Question

Simplify the expression

4 x^{2} - 12000 x^{6}

Evaluate

4 x^{2} - 480 x^{6} \times 25

Solution

4 x^{2} - 12000 x^{6}

Show Solution

4 x^{2} (1 - 3000 x^{4})

Evaluate

4 x^{2} - 480 x^{6} \times 25

Multiply the terms

4 x^{2} - 12000 x^{6}

Rewrite the expression

4 x^{2} - 4 x^{2} \times 3000 x^{4}

Solution

4 x^{2} (1 - 3000 x^{4})

Show Solution

x_{1} = - \frac{4 300 0 ^{3}}{3000}, x_{2} = 0, x_{3} = \frac{4 300 0 ^{3}}{3000}

Alternative Form

x_{1} \approx - 0.13512, x_{2} = 0, x_{3} \approx 0.13512

Evaluate

4 x^{2} - 480 x^{6} \times 25

To find the roots of the expression,set the expression equal to 0

4 x^{2} - 480 x^{6} \times 25 = 0

Multiply the terms

4 x^{2} - 12000 x^{6} = 0

Factor the expression

4 x^{2} (1 - 3000 x^{4}) = 0

Divide both sides

x^{2} (1 - 3000 x^{4}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 1 - 3000 x^{4} = 0

The only way a power can be 0 is when the base equals 0

x = 0 1 - 3000 x^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 3000 x^{4} = 0

Move the constant to the right-hand side and change its sign

- 3000 x^{4} = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

- 3000 x^{4} = - 1

Change the signs on both sides of the equation

3000 x^{4} = 1

Divide both sides

\frac{3000 x ^{4}}{3000} = \frac{1}{3000}

Divide the numbers

x^{4} = \frac{1}{3000}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{1}{3000}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{3000}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 1}{4 3000}

Simplify the radical expression

\frac{1}{4 3000}

Multiply by the Conjugate

\frac{4 300 0 ^{3}}{4 3000 \times 4 300 0 ^{3}}

Multiply the numbers

\frac{4 300 0 ^{3}}{3000}

x = \pm \frac{4 300 0 ^{3}}{3000}

Separate the equation into 2 possible cases

x = \frac{4 300 0 ^{3}}{3000} x = - \frac{4 300 0 ^{3}}{3000}

x = 0 x = \frac{4 300 0 ^{3}}{3000} x = - \frac{4 300 0 ^{3}}{3000}

Solution

x_{1} = - \frac{4 300 0 ^{3}}{3000}, x_{2} = 0, x_{3} = \frac{4 300 0 ^{3}}{3000}

Alternative Form

x_{1} \approx - 0.13512, x_{2} = 0, x_{3} \approx 0.13512

Show Solution