Solve p* p^2 16p-17=0

Question

p \times p^{2} \times 16 p - 17 = 0

Solve the equation

p_{1} = - \frac{4 17}{2}, p_{2} = \frac{4 17}{2}

Alternative Form

p_{1} \approx - 1.015272, p_{2} \approx 1.015272

Evaluate

p \times p^{2} \times 16 p - 17 = 0

Multiply

More Steps

Evaluate

p \times p^{2} \times 16 p

Multiply the terms with the same base by adding their exponents

p^{1 + 2 + 1} \times 16

Add the numbers

p^{4} \times 16

Use the commutative property to reorder the terms

16 p^{4}

16 p^{4} - 17 = 0

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

16 p^{4} = 0 + 17

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

16 p^{4} = 17

Divide both sides

\frac{16 p ^{4}}{16} = \frac{17}{16}

Divide the numbers

p^{4} = \frac{17}{16}

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

p = \pm 4 \frac{17}{16}

Simplify the expression

More Steps

Evaluate

4 \frac{17}{16}

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

\frac{4 17}{4 16}

Simplify the radical expression

More Steps

Evaluate

416

Write the number in exponential form with the base of 2

4 2^{4}

Reduce the index of the radical and exponent with 4

2

\frac{4 17}{2}

p = \pm \frac{4 17}{2}

Separate the equation into 2 possible cases

p = \frac{4 17}{2} p = - \frac{4 17}{2}

Solution

p_{1} = - \frac{4 17}{2}, p_{2} = \frac{4 17}{2}

Alternative Form

p_{1} \approx - 1.015272, p_{2} \approx 1.015272

Show Solution