Solve by Factoring x^2-3x+16=7x

$x^{2} - 3 x + 16 = 7 x$

Step 1

Subtract $7 x$ from both sides of the equation.

$x^{2} - 3 x + 16 - 7 x = 0$

Step 2

Subtract $7 x$ from $- 3 x$ .

$x^{2} - 10 x + 16 = 0$

Step 3

Factor $x^{2} - 10 x + 16$ 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 $16$ and whose sum is $- 10$ .

$- 8, - 2$

Write the factored form using these integers.

$(x - 8) (x - 2) = 0$

Step 4

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

$x - 8 = 0$

$x - 2 = 0$

Step 5

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Add $8$ to both sides of the equation.

$x = 8$

Step 6

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 7

The final solution is all the values that make $(x - 8) (x - 2) = 0$ true.

$x = 8, 2$

Solve by Factoring x^2-3x+16=7x

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