Solve 1-9w^2 - ScanMath

Question

Factor the expression

(1 - 3 w) (1 + 3 w)

Evaluate

1 - 9 w^{2}

Rewrite the expression in exponential form

1^{2} - (3 w)^{2}

Solution

(1 - 3 w) (1 + 3 w)

Show Solution

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

Alternative Form

w_{1} = - 0. \dot{3}, w_{2} = 0. \dot{3}

Evaluate

1 - 9 w^{2}

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

1 - 9 w^{2} = 0

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

- 9 w^{2} = 0 - 1

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

- 9 w^{2} = - 1

Change the signs on both sides of the equation

9 w^{2} = 1

Divide both sides

\frac{9 w ^{2}}{9} = \frac{1}{9}

Divide the numbers

w^{2} = \frac{1}{9}

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

w = \pm \frac{1}{9}

Simplify the expression

More Steps

Evaluate

\frac{1}{9}

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

\frac{1}{9}

Simplify the radical expression

\frac{1}{9}

Simplify the radical expression

More Steps

Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{1}{3}

w = \pm \frac{1}{3}

Separate the equation into 2 possible cases

w = \frac{1}{3} w = - \frac{1}{3}

Solution

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

Alternative Form

w_{1} = - 0. \dot{3}, w_{2} = 0. \dot{3}

Show Solution