Solve 9w^2 - 49 - ScanMath

Question

Factor the expression

(3 w - 7) (3 w + 7)

Evaluate

9 w^{2} - 49

Rewrite the expression in exponential form

(3 w)^{2} - 7^{2}

Solution

(3 w - 7) (3 w + 7)

Show Solution

w_{1} = - \frac{7}{3}, w_{2} = \frac{7}{3}

Alternative Form

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

Evaluate

9 w^{2} - 49

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

9 w^{2} - 49 = 0

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

9 w^{2} = 0 + 49

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

9 w^{2} = 49

Divide both sides

\frac{9 w ^{2}}{9} = \frac{49}{9}

Divide the numbers

w^{2} = \frac{49}{9}

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

w = \pm \frac{49}{9}

Simplify the expression

More Steps

Evaluate

\frac{49}{9}

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

\frac{49}{9}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 7

7^{2}

Reduce the index of the radical and exponent with 2

7

\frac{7}{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{7}{3}

w = \pm \frac{7}{3}

Separate the equation into 2 possible cases

w = \frac{7}{3} w = - \frac{7}{3}

Solution

w_{1} = - \frac{7}{3}, w_{2} = \frac{7}{3}

Alternative Form

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

Show Solution