Solve 5x^(2) 16x-52

Question

5 x^{2} \times 16 x - 52

Simplify the expression

80 x^{3} - 52

Evaluate

5 x^{2} \times 16 x - 52

Solution

More Steps

Evaluate

5 x^{2} \times 16 x

Multiply the terms

80 x^{2} \times x

Multiply the terms with the same base by adding their exponents

80 x^{2 + 1}

Add the numbers

80 x^{3}

80 x^{3} - 52

Show Solution

Factor the expression

4 (20 x^{3} - 13)

Evaluate

5 x^{2} \times 16 x - 52

Multiply

More Steps

Evaluate

5 x^{2} \times 16 x

Multiply the terms

80 x^{2} \times x

Multiply the terms with the same base by adding their exponents

80 x^{2 + 1}

Add the numbers

80 x^{3}

80 x^{3} - 52

Solution

4 (20 x^{3} - 13)

Show Solution

Find the roots

x = \frac{3 650}{10}

Alternative Form

x \approx 0.866239

Evaluate

5 x^{2} \times 16 x - 52

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

5 x^{2} \times 16 x - 52 = 0

Multiply

More Steps

Multiply the terms

5 x^{2} \times 16 x

Multiply the terms

80 x^{2} \times x

Multiply the terms with the same base by adding their exponents

80 x^{2 + 1}

Add the numbers

80 x^{3}

80 x^{3} - 52 = 0

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

80 x^{3} = 0 + 52

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

80 x^{3} = 52

Divide both sides

\frac{80 x ^{3}}{80} = \frac{52}{80}

Divide the numbers

x^{3} = \frac{52}{80}

Cancel out the common factor 4

x^{3} = \frac{13}{20}

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

3 x^{3} = 3 \frac{13}{20}

Calculate

x = 3 \frac{13}{20}

Solution

More Steps

Evaluate

3 \frac{13}{20}

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

\frac{3 13}{3 20}

Multiply by the Conjugate

\frac{3 13 \times 3 2 0 ^{2}}{3 20 \times 3 2 0 ^{2}}

Simplify

\frac{3 13 \times 2 3 50}{3 20 \times 3 2 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

313 \times 2350

Multiply the terms

3650 \times 2

Use the commutative property to reorder the terms

23650

\frac{2 3 650}{3 20 \times 3 2 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

320 \times 3 2 0^{2}

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

3 20 \times 2 0^{2}

Calculate the product

3 2 0^{3}

Reduce the index of the radical and exponent with 3

20

\frac{2 3 650}{20}

Cancel out the common factor 2

\frac{3 650}{10}

x = \frac{3 650}{10}

Alternative Form

x \approx 0.866239

Show Solution