Solve by Factoring 2x^2-12x+32=x^2

$2 x^{2} - 12 x + 32 = x^{2}$

Step 1

Subtract $x^{2}$ from both sides of the equation.

$2 x^{2} - 12 x + 32 - x^{2} = 0$

Step 2

Subtract $x^{2}$ from $2 x^{2}$ .

$x^{2} - 12 x + 32 = 0$

Step 3

Factor $x^{2} - 12 x + 32$ 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 $32$ and whose sum is $- 12$ .

$- 8, - 4$

Write the factored form using these integers.

$(x - 8) (x - 4) = 0$

Step 4

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

$x - 8 = 0$

$x - 4 = 0$

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 $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Step 7

The final solution is all the values that make $(x - 8) (x - 4) = 0$ true.

$x = 8, 4$

Solve by Factoring 2x^2-12x+32=x^2

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