Solve p^2 2p-33=0

Question

Solve the equation

p = \frac{3 132}{2}

Alternative Form

p \approx 2.545822

Evaluate

p^{2} \times 2 p - 33 = 0

Multiply

More Steps

Evaluate

p^{2} \times 2 p

Multiply the terms with the same base by adding their exponents

p^{2 + 1} \times 2

Add the numbers

p^{3} \times 2

Use the commutative property to reorder the terms

2 p^{3}

2 p^{3} - 33 = 0

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

2 p^{3} = 0 + 33

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

2 p^{3} = 33

Divide both sides

\frac{2 p ^{3}}{2} = \frac{33}{2}

Divide the numbers

p^{3} = \frac{33}{2}

Take the 3 -th root on both sides of the equation

3 p^{3} = 3 \frac{33}{2}

Calculate

p = 3 \frac{33}{2}

Solution

More Steps

Evaluate

3 \frac{33}{2}

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

\frac{3 33}{3 2}

Multiply by the Conjugate

\frac{3 33 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 33 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

333 \times 34

The product of roots with the same index is equal to the root of the product

3 33 \times 4

Calculate the product

3132

\frac{3 132}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

The product of roots with the same index is equal to the root of the product

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 132}{2}

p = \frac{3 132}{2}

Alternative Form

p \approx 2.545822

Show Solution