Solve 6p^2 - 8p^6 = 0

Question

Solve the equation

p_{1} = - \frac{4 12}{2}, p_{2} = 0, p_{3} = \frac{4 12}{2}

Alternative Form

p_{1} \approx - 0.930605, p_{2} = 0, p_{3} \approx 0.930605

Evaluate

6 p^{2} - 8 p^{6} = 0

Factor the expression

2 p^{2} (3 - 4 p^{4}) = 0

Divide both sides

p^{2} (3 - 4 p^{4}) = 0

Separate the equation into 2 possible cases

p^{2} = 0 3 - 4 p^{4} = 0

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

p = 0 3 - 4 p^{4} = 0

Solve the equation

More Steps

Evaluate

3 - 4 p^{4} = 0

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

- 4 p^{4} = 0 - 3

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

- 4 p^{4} = - 3

Change the signs on both sides of the equation

4 p^{4} = 3

Divide both sides

\frac{4 p ^{4}}{4} = \frac{3}{4}

Divide the numbers

p^{4} = \frac{3}{4}

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

p = \pm 4 \frac{3}{4}

Simplify the expression

More Steps

Evaluate

4 \frac{3}{4}

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

\frac{4 3}{4 4}

Simplify the radical expression

\frac{4 3}{2}

Multiply by the Conjugate

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

Multiply the numbers

\frac{4 12}{2 \times 2}

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

\frac{4 12}{2}

p = \pm \frac{4 12}{2}

Separate the equation into 2 possible cases

p = \frac{4 12}{2} p = - \frac{4 12}{2}

p = 0 p = \frac{4 12}{2} p = - \frac{4 12}{2}

Solution

p_{1} = - \frac{4 12}{2}, p_{2} = 0, p_{3} = \frac{4 12}{2}

Alternative Form

p_{1} \approx - 0.930605, p_{2} = 0, p_{3} \approx 0.930605

Show Solution