Solve m^250-10151

Question

Simplify the expression

50 m^{2} - 10151

Evaluate

m^{2} \times 50 - 10151

Solution

50 m^{2} - 10151

Show Solution

m_{1} = - \frac{20302}{10}, m_{2} = \frac{20302}{10}

Alternative Form

m_{1} \approx - 14.248509, m_{2} \approx 14.248509

Evaluate

m^{2} \times 50 - 10151

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

m^{2} \times 50 - 10151 = 0

Use the commutative property to reorder the terms

50 m^{2} - 10151 = 0

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

50 m^{2} = 0 + 10151

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

50 m^{2} = 10151

Divide both sides

\frac{50 m ^{2}}{50} = \frac{10151}{50}

Divide the numbers

m^{2} = \frac{10151}{50}

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

m = \pm \frac{10151}{50}

Simplify the expression

More Steps

Evaluate

\frac{10151}{50}

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

\frac{10151}{50}

Simplify the radical expression

More Steps

Evaluate

50

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

25 \times 2

Write the number in exponential form with the base of 5

5^{2} \times 2

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

5^{2} \times 2

Reduce the index of the radical and exponent with 2

52

\frac{10151}{5 2}

Multiply by the Conjugate

\frac{10151 \times 2}{5 2 \times 2}

Multiply the numbers

More Steps

Evaluate

10151 \times 2

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

10151 \times 2

Calculate the product

20302

\frac{20302}{5 2 \times 2}

Multiply the numbers

More Steps

Evaluate

52 \times 2

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

5 \times 2

Multiply the terms

10

\frac{20302}{10}

m = \pm \frac{20302}{10}

Separate the equation into 2 possible cases

m = \frac{20302}{10} m = - \frac{20302}{10}

Solution

m_{1} = - \frac{20302}{10}, m_{2} = \frac{20302}{10}

Alternative Form

m_{1} \approx - 14.248509, m_{2} \approx 14.248509

Show Solution