Solve m^25988/4-111

Question

Simplify the expression

1497 m^{2} - 111

Evaluate

m^{2} \times \frac{5988}{4} - 111

Divide the terms

More Steps

Evaluate

\frac{5988}{4}

Reduce the numbers

\frac{1497}{1}

Calculate

1497

m^{2} \times 1497 - 111

Solution

1497 m^{2} - 111

Show Solution

Factor the expression

3 (499 m^{2} - 37)

Evaluate

m^{2} \times \frac{5988}{4} - 111

Divide the terms

More Steps

Evaluate

\frac{5988}{4}

Reduce the numbers

\frac{1497}{1}

Calculate

1497

m^{2} \times 1497 - 111

Use the commutative property to reorder the terms

1497 m^{2} - 111

Solution

3 (499 m^{2} - 37)

Show Solution

Find the roots

m_{1} = - \frac{18463}{499}, m_{2} = \frac{18463}{499}

Alternative Form

m_{1} \approx - 0.272302, m_{2} \approx 0.272302

Evaluate

m^{2} \times \frac{5988}{4} - 111

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

m^{2} \times \frac{5988}{4} - 111 = 0

Divide the terms

More Steps

Evaluate

\frac{5988}{4}

Reduce the numbers

\frac{1497}{1}

Calculate

1497

m^{2} \times 1497 - 111 = 0

Use the commutative property to reorder the terms

1497 m^{2} - 111 = 0

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

1497 m^{2} = 0 + 111

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

1497 m^{2} = 111

Divide both sides

\frac{1497 m ^{2}}{1497} = \frac{111}{1497}

Divide the numbers

m^{2} = \frac{111}{1497}

Cancel out the common factor 3

m^{2} = \frac{37}{499}

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

m = \pm \frac{37}{499}

Simplify the expression

More Steps

Evaluate

\frac{37}{499}

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

\frac{37}{499}

Multiply by the Conjugate

\frac{37 \times 499}{499 \times 499}

Multiply the numbers

More Steps

Evaluate

37 \times 499

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

37 \times 499

Calculate the product

18463

\frac{18463}{499 \times 499}

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

\frac{18463}{499}

m = \pm \frac{18463}{499}

Separate the equation into 2 possible cases

m = \frac{18463}{499} m = - \frac{18463}{499}

Solution

m_{1} = - \frac{18463}{499}, m_{2} = \frac{18463}{499}

Alternative Form

m_{1} \approx - 0.272302, m_{2} \approx 0.272302

Show Solution