Solve 9w^2005-30 - ScanMath

Question

Simplify the expression

45 w^{2} - 30

Evaluate

9 w^{2} \times 5 - 30

Solution

45 w^{2} - 30

Show Solution

15 (3 w^{2} - 2)

Evaluate

9 w^{2} \times 5 - 30

Multiply the terms

45 w^{2} - 30

Solution

15 (3 w^{2} - 2)

Show Solution

w_{1} = - \frac{6}{3}, w_{2} = \frac{6}{3}

Alternative Form

w_{1} \approx - 0.816497, w_{2} \approx 0.816497

Evaluate

9 w^{2} \times 5 - 30

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

9 w^{2} \times 5 - 30 = 0

Multiply the terms

45 w^{2} - 30 = 0

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

45 w^{2} = 0 + 30

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

45 w^{2} = 30

Divide both sides

\frac{45 w ^{2}}{45} = \frac{30}{45}

Divide the numbers

w^{2} = \frac{30}{45}

Cancel out the common factor 15

w^{2} = \frac{2}{3}

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

w = \pm \frac{2}{3}

Simplify the expression

More Steps

Evaluate

\frac{2}{3}

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

\frac{2}{3}

Multiply by the Conjugate

\frac{2 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

2 \times 3

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

2 \times 3

Calculate the product

6

\frac{6}{3 \times 3}

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

\frac{6}{3}

w = \pm \frac{6}{3}

Separate the equation into 2 possible cases

w = \frac{6}{3} w = - \frac{6}{3}

Solution

w_{1} = - \frac{6}{3}, w_{2} = \frac{6}{3}

Alternative Form

w_{1} \approx - 0.816497, w_{2} \approx 0.816497

Show Solution