Solve 2024 - 2025 o^2024/2025

Question

Simplify the expression

2024 - 24 o^{2}

Evaluate

2024 - 2025 o^{2} \times \frac{24}{2025}

Cancel out the common factor 3

2024 - 2025 o^{2} \times \frac{8}{675}

Solution

More Steps

Multiply the terms

2025 o^{2} \times \frac{8}{675}

Multiply the terms

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Evaluate

2025 \times \frac{8}{675}

Reduce the numbers

3 \times 8

Multiply the numbers

24

24 o^{2}

2024 - 24 o^{2}

Show Solution

Factor the expression

8 (253 - 3 o^{2})

Evaluate

2024 - 2025 o^{2} \times \frac{24}{2025}

Cancel out the common factor 3

2024 - 2025 o^{2} \times \frac{8}{675}

Multiply the terms

More Steps

Multiply the terms

2025 o^{2} \times \frac{8}{675}

Multiply the terms

More Steps

Evaluate

2025 \times \frac{8}{675}

Reduce the numbers

3 \times 8

Multiply the numbers

24

24 o^{2}

2024 - 24 o^{2}

Solution

8 (253 - 3 o^{2})

Show Solution

Find the roots

o_{1} = - \frac{759}{3}, o_{2} = \frac{759}{3}

Alternative Form

o_{1} \approx - 9.183318, o_{2} \approx 9.183318

Evaluate

2024 - 2025 o^{2} \times \frac{24}{2025}

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

2024 - 2025 o^{2} \times \frac{24}{2025} = 0

Cancel out the common factor 3

2024 - 2025 o^{2} \times \frac{8}{675} = 0

Multiply the terms

More Steps

Multiply the terms

2025 o^{2} \times \frac{8}{675}

Multiply the terms

More Steps

Evaluate

2025 \times \frac{8}{675}

Reduce the numbers

3 \times 8

Multiply the numbers

24

24 o^{2}

2024 - 24 o^{2} = 0

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

- 24 o^{2} = 0 - 2024

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

- 24 o^{2} = - 2024

Change the signs on both sides of the equation

24 o^{2} = 2024

Divide both sides

\frac{24 o ^{2}}{24} = \frac{2024}{24}

Divide the numbers

o^{2} = \frac{2024}{24}

Cancel out the common factor 8

o^{2} = \frac{253}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

o = \pm \frac{253}{3}

Simplify the expression

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Evaluate

\frac{253}{3}

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

\frac{253}{3}

Multiply by the Conjugate

\frac{253 \times 3}{3 \times 3}

Multiply the numbers

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Evaluate

253 \times 3

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

253 \times 3

Calculate the product

759

\frac{759}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{759}{3}

o = \pm \frac{759}{3}

Separate the equation into 2 possible cases

o = \frac{759}{3} o = - \frac{759}{3}

Solution

o_{1} = - \frac{759}{3}, o_{2} = \frac{759}{3}

Alternative Form

o_{1} \approx - 9.183318, o_{2} \approx 9.183318

Show Solution