Solve m^24308/2-525

Question

Simplify the expression

2154 m^{2} - 525

Evaluate

m^{2} \times \frac{4308}{2} - 525

Divide the terms

More Steps

Evaluate

\frac{4308}{2}

Reduce the numbers

\frac{2154}{1}

Calculate

2154

m^{2} \times 2154 - 525

Solution

2154 m^{2} - 525

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Factor the expression

3 (718 m^{2} - 175)

Evaluate

m^{2} \times \frac{4308}{2} - 525

Divide the terms

More Steps

Evaluate

\frac{4308}{2}

Reduce the numbers

\frac{2154}{1}

Calculate

2154

m^{2} \times 2154 - 525

Use the commutative property to reorder the terms

2154 m^{2} - 525

Solution

3 (718 m^{2} - 175)

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Find the roots

m_{1} = - \frac{5 5026}{718}, m_{2} = \frac{5 5026}{718}

Alternative Form

m_{1} \approx - 0.493693, m_{2} \approx 0.493693

Evaluate

m^{2} \times \frac{4308}{2} - 525

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

m^{2} \times \frac{4308}{2} - 525 = 0

Divide the terms

More Steps

Evaluate

\frac{4308}{2}

Reduce the numbers

\frac{2154}{1}

Calculate

2154

m^{2} \times 2154 - 525 = 0

Use the commutative property to reorder the terms

2154 m^{2} - 525 = 0

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

2154 m^{2} = 0 + 525

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

2154 m^{2} = 525

Divide both sides

\frac{2154 m ^{2}}{2154} = \frac{525}{2154}

Divide the numbers

m^{2} = \frac{525}{2154}

Cancel out the common factor 3

m^{2} = \frac{175}{718}

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

m = \pm \frac{175}{718}

Simplify the expression

More Steps

Evaluate

\frac{175}{718}

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

\frac{175}{718}

Simplify the radical expression

More Steps

Evaluate

175

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

25 \times 7

Write the number in exponential form with the base of 5

5^{2} \times 7

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

5^{2} \times 7

Reduce the index of the radical and exponent with 2

57

\frac{5 7}{718}

Multiply by the Conjugate

\frac{5 7 \times 718}{718 \times 718}

Multiply the numbers

More Steps

Evaluate

7 \times 718

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

7 \times 718

Calculate the product

5026

\frac{5 5026}{718 \times 718}

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

\frac{5 5026}{718}

m = \pm \frac{5 5026}{718}

Separate the equation into 2 possible cases

m = \frac{5 5026}{718} m = - \frac{5 5026}{718}

Solution

m_{1} = - \frac{5 5026}{718}, m_{2} = \frac{5 5026}{718}

Alternative Form

m_{1} \approx - 0.493693, m_{2} \approx 0.493693

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