Solve 64x^2-40x^4

Question

Factor the expression

8 x^{2} (8 - 5 x^{2})

Evaluate

64 x^{2} - 40 x^{4}

Rewrite the expression

8 x^{2} \times 8 - 8 x^{2} \times 5 x^{2}

Solution

8 x^{2} (8 - 5 x^{2})

Show Solution

x_{1} = - \frac{2 10}{5}, x_{2} = 0, x_{3} = \frac{2 10}{5}

Alternative Form

x_{1} \approx - 1.264911, x_{2} = 0, x_{3} \approx 1.264911

Evaluate

64 x^{2} - 40 x^{4}

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

64 x^{2} - 40 x^{4} = 0

Factor the expression

8 x^{2} (8 - 5 x^{2}) = 0

Divide both sides

x^{2} (8 - 5 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 8 - 5 x^{2} = 0

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

x = 0 8 - 5 x^{2} = 0

Solve the equation

More Steps

Evaluate

8 - 5 x^{2} = 0

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

- 5 x^{2} = 0 - 8

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

- 5 x^{2} = - 8

Change the signs on both sides of the equation

5 x^{2} = 8

Divide both sides

\frac{5 x ^{2}}{5} = \frac{8}{5}

Divide the numbers

x^{2} = \frac{8}{5}

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

x = \pm \frac{8}{5}

Simplify the expression

More Steps

Evaluate

\frac{8}{5}

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

\frac{8}{5}

Simplify the radical expression

\frac{2 2}{5}

Multiply by the Conjugate

\frac{2 2 \times 5}{5 \times 5}

Multiply the numbers

\frac{2 10}{5 \times 5}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{2 10}{5}

x = \pm \frac{2 10}{5}

Separate the equation into 2 possible cases

x = \frac{2 10}{5} x = - \frac{2 10}{5}

x = 0 x = \frac{2 10}{5} x = - \frac{2 10}{5}

Solution

x_{1} = - \frac{2 10}{5}, x_{2} = 0, x_{3} = \frac{2 10}{5}

Alternative Form

x_{1} \approx - 1.264911, x_{2} = 0, x_{3} \approx 1.264911

Show Solution