Solve 15x^2 16x-15

Question

Simplify the expression

240 x^{3} - 15

Evaluate

15 x^{2} \times 16 x - 15

Solution

More Steps

Evaluate

15 x^{2} \times 16 x

Multiply the terms

240 x^{2} \times x

Multiply the terms with the same base by adding their exponents

240 x^{2 + 1}

Add the numbers

240 x^{3}

240 x^{3} - 15

Show Solution

Factor the expression

15 (16 x^{3} - 1)

Evaluate

15 x^{2} \times 16 x - 15

Multiply

More Steps

Evaluate

15 x^{2} \times 16 x

Multiply the terms

240 x^{2} \times x

Multiply the terms with the same base by adding their exponents

240 x^{2 + 1}

Add the numbers

240 x^{3}

240 x^{3} - 15

Solution

15 (16 x^{3} - 1)

Show Solution

Find the roots

x = \frac{3 4}{4}

Alternative Form

x \approx 0.39685

Evaluate

15 x^{2} \times 16 x - 15

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

15 x^{2} \times 16 x - 15 = 0

Multiply

More Steps

Multiply the terms

15 x^{2} \times 16 x

Multiply the terms

240 x^{2} \times x

Multiply the terms with the same base by adding their exponents

240 x^{2 + 1}

Add the numbers

240 x^{3}

240 x^{3} - 15 = 0

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

240 x^{3} = 0 + 15

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

240 x^{3} = 15

Divide both sides

\frac{240 x ^{3}}{240} = \frac{15}{240}

Divide the numbers

x^{3} = \frac{15}{240}

Cancel out the common factor 15

x^{3} = \frac{1}{16}

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

3 x^{3} = 3 \frac{1}{16}

Calculate

x = 3 \frac{1}{16}

Solution

More Steps

Evaluate

3 \frac{1}{16}

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

\frac{3 1}{3 16}

Simplify the radical expression

\frac{1}{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{1}{2 3 2}

Multiply by the Conjugate

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

Simplify

\frac{3 4}{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 4}{4}

x = \frac{3 4}{4}

Alternative Form

x \approx 0.39685

Show Solution