Solve by Factoring 4x^2=49

$4 x^{2} = 49$

Step 1

Subtract $49$ from both sides of the equation.

$4 x^{2} - 49 = 0$

Step 2

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

${(2 x)}^{2} - 49 = 0$

Step 3

Rewrite $49$ as $7^{2}$ .

${(2 x)}^{2} - 7^{2} = 0$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 x$ and $b = 7$ .

$(2 x + 7) (2 x - 7) = 0$

Step 5

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

$2 x + 7 = 0$

$2 x - 7 = 0$

Step 6

Set $2 x + 7$ equal to $0$ and solve for $x$ .

Set $2 x + 7$ equal to $0$ .

$2 x + 7 = 0$

Solve $2 x + 7 = 0$ for $x$ .

Subtract $7$ from both sides of the equation.

$2 x = - 7$

Divide each term in $2 x = - 7$ by $2$ and simplify.

Divide each term in $2 x = - 7$ by $2$ .

$\frac{2 x}{2} = \frac{- 7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 7}{2}$

Divide $x$ by $1$ .

$x = \frac{- 7}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{7}{2}$

Step 7

Set $2 x - 7$ equal to $0$ and solve for $x$ .

Set $2 x - 7$ equal to $0$ .

$2 x - 7 = 0$

Solve $2 x - 7 = 0$ for $x$ .

Add $7$ to both sides of the equation.

$2 x = 7$

Divide each term in $2 x = 7$ by $2$ and simplify.

Divide each term in $2 x = 7$ by $2$ .

$\frac{2 x}{2} = \frac{7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{7}{2}$

Divide $x$ by $1$ .

$x = \frac{7}{2}$

Step 8

The final solution is all the values that make $(2 x + 7) (2 x - 7) = 0$ true.

$x = - \frac{7}{2}, \frac{7}{2}$

Solve by Factoring 4x^2=49

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