Solve p^2 14p - 32 = 0

Question

Solve the equation

p = \frac{2 3 98}{7}

Alternative Form

p \approx 1.317268

Evaluate

p^{2} \times 14 p - 32 = 0

Multiply

More Steps

Evaluate

p^{2} \times 14 p

Multiply the terms with the same base by adding their exponents

p^{2 + 1} \times 14

Add the numbers

p^{3} \times 14

Use the commutative property to reorder the terms

14 p^{3}

14 p^{3} - 32 = 0

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

14 p^{3} = 0 + 32

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

14 p^{3} = 32

Divide both sides

\frac{14 p ^{3}}{14} = \frac{32}{14}

Divide the numbers

p^{3} = \frac{32}{14}

Cancel out the common factor 2

p^{3} = \frac{16}{7}

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

3 p^{3} = 3 \frac{16}{7}

Calculate

p = 3 \frac{16}{7}

Solution

More Steps

Evaluate

3 \frac{16}{7}

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

\frac{3 16}{3 7}

Simplify the radical expression

More Steps

Evaluate

316

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 2

Write the number in exponential form with the base of 2

3 2^{3} \times 2

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 32

Reduce the index of the radical and exponent with 3

232

\frac{2 3 2}{3 7}

Multiply by the Conjugate

\frac{2 3 2 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{2 3 2 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 349

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

3 2 \times 49

Calculate the product

398

\frac{2 3 98}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{2 3 98}{7}

p = \frac{2 3 98}{7}

Alternative Form

p \approx 1.317268

Show Solution