Solve x^213x-48 - ScanMath

Question

Simplify the expression

13 x^{3} - 48

Evaluate

x^{2} \times 13 x - 48

Solution

More Steps

Evaluate

x^{2} \times 13 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 13

Add the numbers

x^{3} \times 13

Use the commutative property to reorder the terms

13 x^{3}

13 x^{3} - 48

Show Solution

x = \frac{2 3 1014}{13}

Alternative Form

x \approx 1.545608

Evaluate

x^{2} \times 13 x - 48

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

x^{2} \times 13 x - 48 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 13 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 13

Add the numbers

x^{3} \times 13

Use the commutative property to reorder the terms

13 x^{3}

13 x^{3} - 48 = 0

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

13 x^{3} = 0 + 48

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

13 x^{3} = 48

Divide both sides

\frac{13 x ^{3}}{13} = \frac{48}{13}

Divide the numbers

x^{3} = \frac{48}{13}

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

3 x^{3} = 3 \frac{48}{13}

Calculate

x = 3 \frac{48}{13}

Solution

More Steps

Evaluate

3 \frac{48}{13}

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

\frac{3 48}{3 13}

Simplify the radical expression

More Steps

Evaluate

348

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

3 8 \times 6

Write the number in exponential form with the base of 2

3 2^{3} \times 6

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

3 2^{3} \times 36

Reduce the index of the radical and exponent with 3

236

\frac{2 3 6}{3 13}

Multiply by the Conjugate

\frac{2 3 6 \times 3 1 3 ^{2}}{3 13 \times 3 1 3 ^{2}}

Simplify

\frac{2 3 6 \times 3 169}{3 13 \times 3 1 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

36 \times 3169

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

3 6 \times 169

Calculate the product

31014

\frac{2 3 1014}{3 13 \times 3 1 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

313 \times 3 1 3^{2}

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

3 13 \times 1 3^{2}

Calculate the product

3 1 3^{3}

Reduce the index of the radical and exponent with 3

13

\frac{2 3 1014}{13}

x = \frac{2 3 1014}{13}

Alternative Form

x \approx 1.545608

Show Solution