Solve 176481-1285 m^2

Question

Find the roots

m_{1} = - \frac{3 25197565}{1285}, m_{2} = \frac{3 25197565}{1285}

Alternative Form

m_{1} \approx - 11.719185, m_{2} \approx 11.719185

Evaluate

176481 - 1285 m^{2}

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

176481 - 1285 m^{2} = 0

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

- 1285 m^{2} = 0 - 176481

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

- 1285 m^{2} = - 176481

Change the signs on both sides of the equation

1285 m^{2} = 176481

Divide both sides

\frac{1285 m ^{2}}{1285} = \frac{176481}{1285}

Divide the numbers

m^{2} = \frac{176481}{1285}

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

m = \pm \frac{176481}{1285}

Simplify the expression

More Steps

Evaluate

\frac{176481}{1285}

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

\frac{176481}{1285}

Simplify the radical expression

More Steps

Evaluate

176481

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

9 \times 19609

Write the number in exponential form with the base of 3

3^{2} \times 19609

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

3^{2} \times 19609

Reduce the index of the radical and exponent with 2

319609

\frac{3 19609}{1285}

Multiply by the Conjugate

\frac{3 19609 \times 1285}{1285 \times 1285}

Multiply the numbers

More Steps

Evaluate

19609 \times 1285

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

19609 \times 1285

Calculate the product

25197565

\frac{3 25197565}{1285 \times 1285}

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

\frac{3 25197565}{1285}

m = \pm \frac{3 25197565}{1285}

Separate the equation into 2 possible cases

m = \frac{3 25197565}{1285} m = - \frac{3 25197565}{1285}

Solution

m_{1} = - \frac{3 25197565}{1285}, m_{2} = \frac{3 25197565}{1285}

Alternative Form

m_{1} \approx - 11.719185, m_{2} \approx 11.719185

Show Solution