Solve u^217u-18=0

Question

Solve the equation

u = \frac{3 5202}{17}

Alternative Form

u \approx 1.019235

Evaluate

u^{2} \times 17 u - 18 = 0

Multiply

More Steps

Evaluate

u^{2} \times 17 u

Multiply the terms with the same base by adding their exponents

u^{2 + 1} \times 17

Add the numbers

u^{3} \times 17

Use the commutative property to reorder the terms

17 u^{3}

17 u^{3} - 18 = 0

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

17 u^{3} = 0 + 18

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

17 u^{3} = 18

Divide both sides

\frac{17 u ^{3}}{17} = \frac{18}{17}

Divide the numbers

u^{3} = \frac{18}{17}

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

3 u^{3} = 3 \frac{18}{17}

Calculate

u = 3 \frac{18}{17}

Solution

More Steps

Evaluate

3 \frac{18}{17}

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

\frac{3 18}{3 17}

Multiply by the Conjugate

\frac{3 18 \times 3 1 7 ^{2}}{3 17 \times 3 1 7 ^{2}}

Simplify

\frac{3 18 \times 3 289}{3 17 \times 3 1 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

318 \times 3289

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

3 18 \times 289

Calculate the product

35202

\frac{3 5202}{3 17 \times 3 1 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

317 \times 3 1 7^{2}

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

3 17 \times 1 7^{2}

Calculate the product

3 1 7^{3}

Reduce the index of the radical and exponent with 3

17

\frac{3 5202}{17}

u = \frac{3 5202}{17}

Alternative Form

u \approx 1.019235

Show Solution