Solve m^25988/2-230

Question

Simplify the expression

2994 m^{2} - 230

Evaluate

m^{2} \times \frac{5988}{2} - 230

Divide the terms

More Steps

Evaluate

\frac{5988}{2}

Reduce the numbers

\frac{2994}{1}

Calculate

2994

m^{2} \times 2994 - 230

Solution

2994 m^{2} - 230

Show Solution

Factor the expression

2 (1497 m^{2} - 115)

Evaluate

m^{2} \times \frac{5988}{2} - 230

Divide the terms

More Steps

Evaluate

\frac{5988}{2}

Reduce the numbers

\frac{2994}{1}

Calculate

2994

m^{2} \times 2994 - 230

Use the commutative property to reorder the terms

2994 m^{2} - 230

Solution

2 (1497 m^{2} - 115)

Show Solution

Find the roots

m_{1} = - \frac{172155}{1497}, m_{2} = \frac{172155}{1497}

Alternative Form

m_{1} \approx - 0.277165, m_{2} \approx 0.277165

Evaluate

m^{2} \times \frac{5988}{2} - 230

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

m^{2} \times \frac{5988}{2} - 230 = 0

Divide the terms

More Steps

Evaluate

\frac{5988}{2}

Reduce the numbers

\frac{2994}{1}

Calculate

2994

m^{2} \times 2994 - 230 = 0

Use the commutative property to reorder the terms

2994 m^{2} - 230 = 0

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

2994 m^{2} = 0 + 230

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

2994 m^{2} = 230

Divide both sides

\frac{2994 m ^{2}}{2994} = \frac{230}{2994}

Divide the numbers

m^{2} = \frac{230}{2994}

Cancel out the common factor 2

m^{2} = \frac{115}{1497}

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

m = \pm \frac{115}{1497}

Simplify the expression

More Steps

Evaluate

\frac{115}{1497}

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

\frac{115}{1497}

Multiply by the Conjugate

\frac{115 \times 1497}{1497 \times 1497}

Multiply the numbers

More Steps

Evaluate

115 \times 1497

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

115 \times 1497

Calculate the product

172155

\frac{172155}{1497 \times 1497}

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

\frac{172155}{1497}

m = \pm \frac{172155}{1497}

Separate the equation into 2 possible cases

m = \frac{172155}{1497} m = - \frac{172155}{1497}

Solution

m_{1} = - \frac{172155}{1497}, m_{2} = \frac{172155}{1497}

Alternative Form

m_{1} \approx - 0.277165, m_{2} \approx 0.277165

Show Solution