Solve x^2024x-2025

Question

Simplify the expression

24 x^{3} - 2025

Evaluate

x^{2} \times 24 x - 2025

Solution

More Steps

Evaluate

x^{2} \times 24 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 24

Add the numbers

x^{3} \times 24

Use the commutative property to reorder the terms

24 x^{3}

24 x^{3} - 2025

Show Solution

Factor the expression

3 (8 x^{3} - 675)

Evaluate

x^{2} \times 24 x - 2025

Multiply

More Steps

Evaluate

x^{2} \times 24 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 24

Add the numbers

x^{3} \times 24

Use the commutative property to reorder the terms

24 x^{3}

24 x^{3} - 2025

Solution

3 (8 x^{3} - 675)

Show Solution

Find the roots

x = \frac{3 3 25}{2}

Alternative Form

x \approx 4.386027

Evaluate

x^{2} \times 24 x - 2025

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

x^{2} \times 24 x - 2025 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 24 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 24

Add the numbers

x^{3} \times 24

Use the commutative property to reorder the terms

24 x^{3}

24 x^{3} - 2025 = 0

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

24 x^{3} = 0 + 2025

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

24 x^{3} = 2025

Divide both sides

\frac{24 x ^{3}}{24} = \frac{2025}{24}

Divide the numbers

x^{3} = \frac{2025}{24}

Cancel out the common factor 3

x^{3} = \frac{675}{8}

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

3 x^{3} = 3 \frac{675}{8}

Calculate

x = 3 \frac{675}{8}

Solution

More Steps

Evaluate

3 \frac{675}{8}

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

\frac{3 675}{3 8}

Simplify the radical expression

More Steps

Evaluate

3675

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

3 27 \times 25

Write the number in exponential form with the base of 3

3 3^{3} \times 25

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

3 3^{3} \times 325

Reduce the index of the radical and exponent with 3

3325

\frac{3 3 25}{3 8}

Simplify the radical expression

More Steps

Evaluate

38

Write the number in exponential form with the base of 2

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 3 25}{2}

x = \frac{3 3 25}{2}

Alternative Form

x \approx 4.386027

Show Solution