Solve x^2 150x-6475

Question

Simplify the expression

150 x^{3} - 6475

Evaluate

x^{2} \times 150 x - 6475

Solution

More Steps

Evaluate

x^{2} \times 150 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 150

Add the numbers

x^{3} \times 150

Use the commutative property to reorder the terms

150 x^{3}

150 x^{3} - 6475

Show Solution

Factor the expression

25 (6 x^{3} - 259)

Evaluate

x^{2} \times 150 x - 6475

Multiply

More Steps

Evaluate

x^{2} \times 150 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 150

Add the numbers

x^{3} \times 150

Use the commutative property to reorder the terms

150 x^{3}

150 x^{3} - 6475

Solution

25 (6 x^{3} - 259)

Show Solution

Find the roots

x = \frac{3 9324}{6}

Alternative Form

x \approx 3.507919

Evaluate

x^{2} \times 150 x - 6475

To find the roots of the expression,set the expression equal to 0

x^{2} \times 150 x - 6475 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 150 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 150

Add the numbers

x^{3} \times 150

Use the commutative property to reorder the terms

150 x^{3}

150 x^{3} - 6475 = 0

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

150 x^{3} = 0 + 6475

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

150 x^{3} = 6475

Divide both sides

\frac{150 x ^{3}}{150} = \frac{6475}{150}

Divide the numbers

x^{3} = \frac{6475}{150}

Cancel out the common factor 25

x^{3} = \frac{259}{6}

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

3 x^{3} = 3 \frac{259}{6}

Calculate

x = 3 \frac{259}{6}

Solution

More Steps

Evaluate

3 \frac{259}{6}

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

\frac{3 259}{3 6}

Multiply by the Conjugate

\frac{3 259 \times 3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Simplify

\frac{3 259 \times 3 36}{3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

3259 \times 336

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

3 259 \times 36

Calculate the product

39324

\frac{3 9324}{3 6 \times 3 6 ^{2}}

Multiply the numbers

More Steps

Evaluate

36 \times 3 6^{2}

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

3 6 \times 6^{2}

Calculate the product

3 6^{3}

Reduce the index of the radical and exponent with 3

6

\frac{3 9324}{6}

x = \frac{3 9324}{6}

Alternative Form

x \approx 3.507919

Show Solution