Solve m^25m -14= 0

Question

Solve the equation

m = \frac{3 350}{5}

Alternative Form

m \approx 1.40946

Evaluate

m^{2} \times 5 m - 14 = 0

Multiply

More Steps

Evaluate

m^{2} \times 5 m

Multiply the terms with the same base by adding their exponents

m^{2 + 1} \times 5

Add the numbers

m^{3} \times 5

Use the commutative property to reorder the terms

5 m^{3}

5 m^{3} - 14 = 0

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

5 m^{3} = 0 + 14

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

5 m^{3} = 14

Divide both sides

\frac{5 m ^{3}}{5} = \frac{14}{5}

Divide the numbers

m^{3} = \frac{14}{5}

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

3 m^{3} = 3 \frac{14}{5}

Calculate

m = 3 \frac{14}{5}

Solution

More Steps

Evaluate

3 \frac{14}{5}

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

\frac{3 14}{3 5}

Multiply by the Conjugate

\frac{3 14 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 14 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

314 \times 325

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

3 14 \times 25

Calculate the product

3350

\frac{3 350}{3 5 \times 3 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 3 5^{2}

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

3 5 \times 5^{2}

Calculate the product

3 5^{3}

Reduce the index of the radical and exponent with 3

5

\frac{3 350}{5}

m = \frac{3 350}{5}

Alternative Form

m \approx 1.40946

Show Solution