Solve a^2 14a-51=0

Question

Solve the equation

a = \frac{3 9996}{14}

Alternative Form

a \approx 1.538677

Evaluate

a^{2} \times 14 a - 51 = 0

Multiply

More Steps

Evaluate

a^{2} \times 14 a

Multiply the terms with the same base by adding their exponents

a^{2 + 1} \times 14

Add the numbers

a^{3} \times 14

Use the commutative property to reorder the terms

14 a^{3}

14 a^{3} - 51 = 0

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

14 a^{3} = 0 + 51

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

14 a^{3} = 51

Divide both sides

\frac{14 a ^{3}}{14} = \frac{51}{14}

Divide the numbers

a^{3} = \frac{51}{14}

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

3 a^{3} = 3 \frac{51}{14}

Calculate

a = 3 \frac{51}{14}

Solution

More Steps

Evaluate

3 \frac{51}{14}

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

\frac{3 51}{3 14}

Multiply by the Conjugate

\frac{3 51 \times 3 1 4 ^{2}}{3 14 \times 3 1 4 ^{2}}

Simplify

\frac{3 51 \times 3 196}{3 14 \times 3 1 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

351 \times 3196

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

3 51 \times 196

Calculate the product

39996

\frac{3 9996}{3 14 \times 3 1 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

314 \times 3 1 4^{2}

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

3 14 \times 1 4^{2}

Calculate the product

3 1 4^{3}

Reduce the index of the radical and exponent with 3

14

\frac{3 9996}{14}

a = \frac{3 9996}{14}

Alternative Form

a \approx 1.538677

Show Solution