Solve by Factoring x^2+14=9x

$x^{2} + 14 = 9 x$

Step 1

Subtract $9 x$ from both sides of the equation.

$x^{2} + 14 - 9 x = 0$

Step 2

Factor $x^{2} + 14 - 9 x$ 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 $14$ and whose sum is $- 9$ .

$- 7, - 2$

Write the factored form using these integers.

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

Step 3

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

$x - 7 = 0$

$x - 2 = 0$

Step 4

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

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

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

Step 5

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

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Step 6

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

$x = 7, 2$

Solve by Factoring x^2+14=9x

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