Solve 2x^2 - 25x^63

Question

Simplify the expression

2 x^{2} - 75 x^{6}

Evaluate

2 x^{2} - 25 x^{6} \times 3

Solution

2 x^{2} - 75 x^{6}

Show Solution

x^{2} (2 - 75 x^{4})

Evaluate

2 x^{2} - 25 x^{6} \times 3

Multiply the terms

2 x^{2} - 75 x^{6}

Rewrite the expression

x^{2} \times 2 - x^{2} \times 75 x^{4}

Solution

x^{2} (2 - 75 x^{4})

Show Solution

x_{1} = - \frac{4 2 \times 7 5 ^{3}}{75}, x_{2} = 0, x_{3} = \frac{4 2 \times 7 5 ^{3}}{75}

Alternative Form

x_{1} \approx - 0.404103, x_{2} = 0, x_{3} \approx 0.404103

Evaluate

2 x^{2} - 25 x^{6} \times 3

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

2 x^{2} - 25 x^{6} \times 3 = 0

Multiply the terms

2 x^{2} - 75 x^{6} = 0

Factor the expression

x^{2} (2 - 75 x^{4}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 2 - 75 x^{4} = 0

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

x = 0 2 - 75 x^{4} = 0

Solve the equation

More Steps

Evaluate

2 - 75 x^{4} = 0

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

- 75 x^{4} = 0 - 2

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

- 75 x^{4} = - 2

Change the signs on both sides of the equation

75 x^{4} = 2

Divide both sides

\frac{75 x ^{4}}{75} = \frac{2}{75}

Divide the numbers

x^{4} = \frac{2}{75}

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

x = \pm 4 \frac{2}{75}

Simplify the expression

More Steps

Evaluate

4 \frac{2}{75}

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

\frac{4 2}{4 75}

Multiply by the Conjugate

\frac{4 2 \times 4 7 5 ^{3}}{4 75 \times 4 7 5 ^{3}}

The product of roots with the same index is equal to the root of the product

\frac{4 2 \times 7 5 ^{3}}{4 75 \times 4 7 5 ^{3}}

Multiply the numbers

\frac{4 2 \times 7 5 ^{3}}{75}

x = \pm \frac{4 2 \times 7 5 ^{3}}{75}

Separate the equation into 2 possible cases

x = \frac{4 2 \times 7 5 ^{3}}{75} x = - \frac{4 2 \times 7 5 ^{3}}{75}

x = 0 x = \frac{4 2 \times 7 5 ^{3}}{75} x = - \frac{4 2 \times 7 5 ^{3}}{75}

Solution

x_{1} = - \frac{4 2 \times 7 5 ^{3}}{75}, x_{2} = 0, x_{3} = \frac{4 2 \times 7 5 ^{3}}{75}

Alternative Form

x_{1} \approx - 0.404103, x_{2} = 0, x_{3} \approx 0.404103

Show Solution