Solve by Factoring x/4-117/(4x)=-1

$\frac{x}{4} - \frac{117}{4 x} = - 1$

Step 1

Add $1$ to both sides of the equation.

$\frac{x}{4} - \frac{117}{4 x} + 1 = 0$

Step 2

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{x}{4} \cdot \frac{x}{x} - \frac{117}{4 x} + 1 = 0$

Step 3

Multiply $\frac{x}{4}$ by $\frac{x}{x}$ .

$\frac{x \cdot x}{4 x} - \frac{117}{4 x} + 1 = 0$

Step 4

Combine the numerators over the common denominator.

$\frac{x \cdot x - 117}{4 x} + 1 = 0$

Step 5

Multiply $x$ by $x$ .

$\frac{x^{2} - 117}{4 x} + 1 = 0$

Step 6

Write $1$ as a fraction with a common denominator.

$\frac{x^{2} - 117}{4 x} + \frac{4 x}{4 x} = 0$

Step 7

Combine the numerators over the common denominator.

$\frac{x^{2} - 117 + 4 x}{4 x} = 0$

Step 8

Factor $x^{2} - 117 + 4 x$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 117$ and whose sum is $4$ .

$- 9, 13$

Write the factored form using these integers.

$\frac{(x - 9) (x + 13)}{4 x} = 0$

Step 9

Set the numerator equal to zero.

$(x - 9) (x + 13) = 0$

Step 10

Solve the equation for $x$ .

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

$x - 9 = 0$

$x + 13 = 0$

Set $x - 9$ equal to $0$ and solve for $x$ .

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

Set $x + 13$ equal to $0$ and solve for $x$ .

Set $x + 13$ equal to $0$ .

$x + 13 = 0$

Subtract $13$ from both sides of the equation.

$x = - 13$

The final solution is all the values that make $(x - 9) (x + 13) = 0$ true.

$x = 9, - 13$

Solve by Factoring x/4-117/(4x)=-1

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