Solve x^2 19x -150

Question

Simplify the expression

19 x^{3} - 150

Evaluate

x^{2} \times 19 x - 150

Solution

More Steps

Evaluate

x^{2} \times 19 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 19

Add the numbers

x^{3} \times 19

Use the commutative property to reorder the terms

19 x^{3}

19 x^{3} - 150

Show Solution

x = \frac{3 54150}{19}

Alternative Form

x \approx 1.991189

Evaluate

x^{2} \times 19 x - 150

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

x^{2} \times 19 x - 150 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 19 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 19

Add the numbers

x^{3} \times 19

Use the commutative property to reorder the terms

19 x^{3}

19 x^{3} - 150 = 0

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

19 x^{3} = 0 + 150

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

19 x^{3} = 150

Divide both sides

\frac{19 x ^{3}}{19} = \frac{150}{19}

Divide the numbers

x^{3} = \frac{150}{19}

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

3 x^{3} = 3 \frac{150}{19}

Calculate

x = 3 \frac{150}{19}

Solution

More Steps

Evaluate

3 \frac{150}{19}

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

\frac{3 150}{3 19}

Multiply by the Conjugate

\frac{3 150 \times 3 1 9 ^{2}}{3 19 \times 3 1 9 ^{2}}

Simplify

\frac{3 150 \times 3 361}{3 19 \times 3 1 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

3150 \times 3361

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

3 150 \times 361

Calculate the product

354150

\frac{3 54150}{3 19 \times 3 1 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

319 \times 3 1 9^{2}

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

3 19 \times 1 9^{2}

Calculate the product

3 1 9^{3}

Reduce the index of the radical and exponent with 3

19

\frac{3 54150}{19}

x = \frac{3 54150}{19}

Alternative Form

x \approx 1.991189

Show Solution