Solve x^2 16x - 225

Question

Simplify the expression

16 x^{3} - 225

Evaluate

x^{2} \times 16 x - 225

Solution

More Steps

Evaluate

x^{2} \times 16 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 16

Add the numbers

x^{3} \times 16

Use the commutative property to reorder the terms

16 x^{3}

16 x^{3} - 225

Show Solution

x = \frac{3 900}{4}

Alternative Form

x \approx 2.413723

Evaluate

x^{2} \times 16 x - 225

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

x^{2} \times 16 x - 225 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 16 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 16

Add the numbers

x^{3} \times 16

Use the commutative property to reorder the terms

16 x^{3}

16 x^{3} - 225 = 0

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

16 x^{3} = 0 + 225

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

16 x^{3} = 225

Divide both sides

\frac{16 x ^{3}}{16} = \frac{225}{16}

Divide the numbers

x^{3} = \frac{225}{16}

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

3 x^{3} = 3 \frac{225}{16}

Calculate

x = 3 \frac{225}{16}

Solution

More Steps

Evaluate

3 \frac{225}{16}

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

\frac{3 225}{3 16}

Simplify the radical expression

More Steps

Evaluate

316

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 2

Write the number in exponential form with the base of 2

3 2^{3} \times 2

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 32

Reduce the index of the radical and exponent with 3

232

\frac{3 225}{2 3 2}

Multiply by the Conjugate

\frac{3 225 \times 3 2 ^{2}}{2 3 2 \times 3 2 ^{2}}

Simplify

\frac{3 225 \times 3 4}{2 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

3225 \times 34

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

3 225 \times 4

Calculate the product

3900

\frac{3 900}{2 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

232 \times 3 2^{2}

Multiply the terms

2 \times 2

Multiply the numbers

4

\frac{3 900}{4}

x = \frac{3 900}{4}

Alternative Form

x \approx 2.413723

Show Solution