Solve 10x^2 - 32x^6

Question

Factor the expression

2 x^{2} (5 - 16 x^{4})

Evaluate

10 x^{2} - 32 x^{6}

Rewrite the expression

2 x^{2} \times 5 - 2 x^{2} \times 16 x^{4}

Solution

2 x^{2} (5 - 16 x^{4})

Show Solution

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

Alternative Form

x_{1} \approx - 0.747674, x_{2} = 0, x_{3} \approx 0.747674

Evaluate

10 x^{2} - 32 x^{6}

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

10 x^{2} - 32 x^{6} = 0

Factor the expression

2 x^{2} (5 - 16 x^{4}) = 0

Divide both sides

x^{2} (5 - 16 x^{4}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 5 - 16 x^{4} = 0

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

x = 0 5 - 16 x^{4} = 0

Solve the equation

More Steps

Evaluate

5 - 16 x^{4} = 0

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

- 16 x^{4} = 0 - 5

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

- 16 x^{4} = - 5

Change the signs on both sides of the equation

16 x^{4} = 5

Divide both sides

\frac{16 x ^{4}}{16} = \frac{5}{16}

Divide the numbers

x^{4} = \frac{5}{16}

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

x = \pm 4 \frac{5}{16}

Simplify the expression

More Steps

Evaluate

4 \frac{5}{16}

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

\frac{4 5}{4 16}

Simplify the radical expression

\frac{4 5}{2}

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

Separate the equation into 2 possible cases

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

x = 0 x = \frac{4 5}{2} x = - \frac{4 5}{2}

Solution

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

Alternative Form

x_{1} \approx - 0.747674, x_{2} = 0, x_{3} \approx 0.747674

Show Solution