Solve m^22520/5-41

Question

Simplify the expression

504 m^{2} - 41

Evaluate

m^{2} \times \frac{2520}{5} - 41

Divide the terms

More Steps

Evaluate

\frac{2520}{5}

Reduce the numbers

\frac{504}{1}

Calculate

504

m^{2} \times 504 - 41

Solution

504 m^{2} - 41

Show Solution

m_{1} = - \frac{574}{84}, m_{2} = \frac{574}{84}

Alternative Form

m_{1} \approx - 0.285218, m_{2} \approx 0.285218

Evaluate

m^{2} \times \frac{2520}{5} - 41

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

m^{2} \times \frac{2520}{5} - 41 = 0

Divide the terms

More Steps

Evaluate

\frac{2520}{5}

Reduce the numbers

\frac{504}{1}

Calculate

504

m^{2} \times 504 - 41 = 0

Use the commutative property to reorder the terms

504 m^{2} - 41 = 0

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

504 m^{2} = 0 + 41

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

504 m^{2} = 41

Divide both sides

\frac{504 m ^{2}}{504} = \frac{41}{504}

Divide the numbers

m^{2} = \frac{41}{504}

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

m = \pm \frac{41}{504}

Simplify the expression

More Steps

Evaluate

\frac{41}{504}

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

\frac{41}{504}

Simplify the radical expression

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Evaluate

504

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

36 \times 14

Write the number in exponential form with the base of 6

6^{2} \times 14

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

6^{2} \times 14

Reduce the index of the radical and exponent with 2

614

\frac{41}{6 14}

Multiply by the Conjugate

\frac{41 \times 14}{6 14 \times 14}

Multiply the numbers

More Steps

Evaluate

41 \times 14

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

41 \times 14

Calculate the product

574

\frac{574}{6 14 \times 14}

Multiply the numbers

More Steps

Evaluate

614 \times 14

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

6 \times 14

Multiply the terms

84

\frac{574}{84}

m = \pm \frac{574}{84}

Separate the equation into 2 possible cases

m = \frac{574}{84} m = - \frac{574}{84}

Solution

m_{1} = - \frac{574}{84}, m_{2} = \frac{574}{84}

Alternative Form

m_{1} \approx - 0.285218, m_{2} \approx 0.285218

Show Solution