Solve by Factoring 4w^2-25=0

$4 w^{2} - 25 = 0$

Step 1

Rewrite $4 w^{2}$ as ${(2 w)}^{2}$ .

${(2 w)}^{2} - 25 = 0$

Step 2

Rewrite $25$ as $5^{2}$ .

${(2 w)}^{2} - 5^{2} = 0$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 w$ and $b = 5$ .

$(2 w + 5) (2 w - 5) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$2 w + 5 = 0$

$2 w - 5 = 0$

Step 5

Set $2 w + 5$ equal to $0$ and solve for $w$ .

Set $2 w + 5$ equal to $0$ .

$2 w + 5 = 0$

Solve $2 w + 5 = 0$ for $w$ .

Subtract $5$ from both sides of the equation.

$2 w = - 5$

Divide each term in $2 w = - 5$ by $2$ and simplify.

Divide each term in $2 w = - 5$ by $2$ .

$\frac{2 w}{2} = \frac{- 5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 w}{2} = \frac{- 5}{2}$

Divide $w$ by $1$ .

$w = \frac{- 5}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$w = - \frac{5}{2}$

Step 6

Set $2 w - 5$ equal to $0$ and solve for $w$ .

Set $2 w - 5$ equal to $0$ .

$2 w - 5 = 0$

Solve $2 w - 5 = 0$ for $w$ .

Add $5$ to both sides of the equation.

$2 w = 5$

Divide each term in $2 w = 5$ by $2$ and simplify.

Divide each term in $2 w = 5$ by $2$ .

$\frac{2 w}{2} = \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 w}{2} = \frac{5}{2}$

Divide $w$ by $1$ .

$w = \frac{5}{2}$

Step 7

The final solution is all the values that make $(2 w + 5) (2 w - 5) = 0$ true.

$w = - \frac{5}{2}, \frac{5}{2}$

Solve by Factoring 4w^2-25=0

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