Solve p^2 14p-38=0

Question

Solve the equation

p = \frac{3 931}{7}

Alternative Form

p \approx 1.394928

Evaluate

p^{2} \times 14 p - 38 = 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} - 38 = 0

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

14 p^{3} = 0 + 38

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

14 p^{3} = 38

Divide both sides

\frac{14 p ^{3}}{14} = \frac{38}{14}

Divide the numbers

p^{3} = \frac{38}{14}

Cancel out the common factor 2

p^{3} = \frac{19}{7}

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

3 p^{3} = 3 \frac{19}{7}

Calculate

p = 3 \frac{19}{7}

Solution

More Steps

Evaluate

3 \frac{19}{7}

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

\frac{3 19}{3 7}

Multiply by the Conjugate

\frac{3 19 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{3 19 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

319 \times 349

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

3 19 \times 49

Calculate the product

3931

\frac{3 931}{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{3 931}{7}

p = \frac{3 931}{7}

Alternative Form

p \approx 1.394928

Show Solution