Solve 40403-6w^2 - ScanMath

Question

Find the roots

w_{1} = - \frac{242418}{6}, w_{2} = \frac{242418}{6}

Alternative Form

w_{1} \approx - 82.059937, w_{2} \approx 82.059937

Evaluate

40403 - 6 w^{2}

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

40403 - 6 w^{2} = 0

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

- 6 w^{2} = 0 - 40403

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

- 6 w^{2} = - 40403

Change the signs on both sides of the equation

6 w^{2} = 40403

Divide both sides

\frac{6 w ^{2}}{6} = \frac{40403}{6}

Divide the numbers

w^{2} = \frac{40403}{6}

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

w = \pm \frac{40403}{6}

Simplify the expression

More Steps

Evaluate

\frac{40403}{6}

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

\frac{40403}{6}

Multiply by the Conjugate

\frac{40403 \times 6}{6 \times 6}

Multiply the numbers

More Steps

Evaluate

40403 \times 6

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

40403 \times 6

Calculate the product

242418

\frac{242418}{6 \times 6}

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

\frac{242418}{6}

w = \pm \frac{242418}{6}

Separate the equation into 2 possible cases

w = \frac{242418}{6} w = - \frac{242418}{6}

Solution

w_{1} = - \frac{242418}{6}, w_{2} = \frac{242418}{6}

Alternative Form

w_{1} \approx - 82.059937, w_{2} \approx 82.059937

Show Solution