Solve m^25988/1-147

Question

Simplify the expression

5988 m^{2} - 147

Evaluate

m^{2} \times \frac{5988}{1} - 147

Divide the terms

m^{2} \times 5988 - 147

Solution

5988 m^{2} - 147

Show Solution

3 (1996 m^{2} - 49)

Evaluate

m^{2} \times \frac{5988}{1} - 147

Divide the terms

m^{2} \times 5988 - 147

Use the commutative property to reorder the terms

5988 m^{2} - 147

Solution

3 (1996 m^{2} - 49)

Show Solution

m_{1} = - \frac{7 499}{998}, m_{2} = \frac{7 499}{998}

Alternative Form

m_{1} \approx - 0.156682, m_{2} \approx 0.156682

Evaluate

m^{2} \times \frac{5988}{1} - 147

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

m^{2} \times \frac{5988}{1} - 147 = 0

Divide the terms

m^{2} \times 5988 - 147 = 0

Use the commutative property to reorder the terms

5988 m^{2} - 147 = 0

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

5988 m^{2} = 0 + 147

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

5988 m^{2} = 147

Divide both sides

\frac{5988 m ^{2}}{5988} = \frac{147}{5988}

Divide the numbers

m^{2} = \frac{147}{5988}

Cancel out the common factor 3

m^{2} = \frac{49}{1996}

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

m = \pm \frac{49}{1996}

Simplify the expression

More Steps

Evaluate

\frac{49}{1996}

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

\frac{49}{1996}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 7

7^{2}

Reduce the index of the radical and exponent with 2

7

\frac{7}{1996}

Simplify the radical expression

More Steps

Evaluate

1996

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

4 \times 499

Write the number in exponential form with the base of 2

2^{2} \times 499

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

2^{2} \times 499

Reduce the index of the radical and exponent with 2

2499

\frac{7}{2 499}

Multiply by the Conjugate

\frac{7 499}{2 499 \times 499}

Multiply the numbers

More Steps

Evaluate

2499 \times 499

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

2 \times 499

Multiply the terms

998

\frac{7 499}{998}

m = \pm \frac{7 499}{998}

Separate the equation into 2 possible cases

m = \frac{7 499}{998} m = - \frac{7 499}{998}

Solution

m_{1} = - \frac{7 499}{998}, m_{2} = \frac{7 499}{998}

Alternative Form

m_{1} \approx - 0.156682, m_{2} \approx 0.156682

Show Solution