Solve 2x^2 -5x^6 - ScanMath

Question

Factor the expression

x^{2} (2 - 5 x^{4})

Evaluate

2 x^{2} - 5 x^{6}

Rewrite the expression

x^{2} \times 2 - x^{2} \times 5 x^{4}

Solution

x^{2} (2 - 5 x^{4})

Show Solution

x_{1} = - \frac{4 250}{5}, x_{2} = 0, x_{3} = \frac{4 250}{5}

Alternative Form

x_{1} \approx - 0.795271, x_{2} = 0, x_{3} \approx 0.795271

Evaluate

2 x^{2} - 5 x^{6}

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

2 x^{2} - 5 x^{6} = 0

Factor the expression

x^{2} (2 - 5 x^{4}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 2 - 5 x^{4} = 0

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

x = 0 2 - 5 x^{4} = 0

Solve the equation

More Steps

Evaluate

2 - 5 x^{4} = 0

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

- 5 x^{4} = 0 - 2

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

- 5 x^{4} = - 2

Change the signs on both sides of the equation

5 x^{4} = 2

Divide both sides

\frac{5 x ^{4}}{5} = \frac{2}{5}

Divide the numbers

x^{4} = \frac{2}{5}

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

x = \pm 4 \frac{2}{5}

Simplify the expression

More Steps

Evaluate

4 \frac{2}{5}

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

\frac{4 2}{4 5}

Multiply by the Conjugate

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

Simplify

\frac{4 2 \times 4 125}{4 5 \times 4 5 ^{3}}

Multiply the numbers

\frac{4 250}{4 5 \times 4 5 ^{3}}

Multiply the numbers

\frac{4 250}{5}

x = \pm \frac{4 250}{5}

Separate the equation into 2 possible cases

x = \frac{4 250}{5} x = - \frac{4 250}{5}

x = 0 x = \frac{4 250}{5} x = - \frac{4 250}{5}

Solution

x_{1} = - \frac{4 250}{5}, x_{2} = 0, x_{3} = \frac{4 250}{5}

Alternative Form

x_{1} \approx - 0.795271, x_{2} = 0, x_{3} \approx 0.795271

Show Solution