Solve m^22520/7-5

Question

Simplify the expression

360 m^{2} - 5

Evaluate

m^{2} \times \frac{2520}{7} - 5

Divide the terms

More Steps

Evaluate

\frac{2520}{7}

Reduce the numbers

\frac{360}{1}

Calculate

360

m^{2} \times 360 - 5

Solution

360 m^{2} - 5

Show Solution

Factor the expression

5 (72 m^{2} - 1)

Evaluate

m^{2} \times \frac{2520}{7} - 5

Divide the terms

More Steps

Evaluate

\frac{2520}{7}

Reduce the numbers

\frac{360}{1}

Calculate

360

m^{2} \times 360 - 5

Use the commutative property to reorder the terms

360 m^{2} - 5

Solution

5 (72 m^{2} - 1)

Show Solution

Find the roots

m_{1} = - \frac{2}{12}, m_{2} = \frac{2}{12}

Alternative Form

m_{1} \approx - 0.117851, m_{2} \approx 0.117851

Evaluate

m^{2} \times \frac{2520}{7} - 5

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

m^{2} \times \frac{2520}{7} - 5 = 0

Divide the terms

More Steps

Evaluate

\frac{2520}{7}

Reduce the numbers

\frac{360}{1}

Calculate

360

m^{2} \times 360 - 5 = 0

Use the commutative property to reorder the terms

360 m^{2} - 5 = 0

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

360 m^{2} = 0 + 5

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

360 m^{2} = 5

Divide both sides

\frac{360 m ^{2}}{360} = \frac{5}{360}

Divide the numbers

m^{2} = \frac{5}{360}

Cancel out the common factor 5

m^{2} = \frac{1}{72}

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

m = \pm \frac{1}{72}

Simplify the expression

More Steps

Evaluate

\frac{1}{72}

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

\frac{1}{72}

Simplify the radical expression

\frac{1}{72}

Simplify the radical expression

More Steps

Evaluate

72

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

36 \times 2

Write the number in exponential form with the base of 6

6^{2} \times 2

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

6^{2} \times 2

Reduce the index of the radical and exponent with 2

62

\frac{1}{6 2}

Multiply by the Conjugate

\frac{2}{6 2 \times 2}

Multiply the numbers

More Steps

Evaluate

62 \times 2

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

6 \times 2

Multiply the terms

12

\frac{2}{12}

m = \pm \frac{2}{12}

Separate the equation into 2 possible cases

m = \frac{2}{12} m = - \frac{2}{12}

Solution

m_{1} = - \frac{2}{12}, m_{2} = \frac{2}{12}

Alternative Form

m_{1} \approx - 0.117851, m_{2} \approx 0.117851

Show Solution