Solve by Factoring x^2+8x-65=x-5

$x^{2} + 8 x - 65 = x - 5$

Step 1

Move all the expressions to the left side of the equation.

Subtract $x$ from both sides of the equation.

$x^{2} + 8 x - 65 - x = - 5$

Add $5$ to both sides of the equation.

$x^{2} + 8 x - 65 - x + 5 = 0$

Step 2

Simplify $x^{2} + 8 x - 65 - x + 5$ .

Subtract $x$ from $8 x$ .

$x^{2} + 7 x - 65 + 5 = 0$

Add $- 65$ and $5$ .

$x^{2} + 7 x - 60 = 0$

Step 3

Factor $x^{2} + 7 x - 60$ 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 $- 60$ and whose sum is $7$ .

$- 5, 12$

Write the factored form using these integers.

$(x - 5) (x + 12) = 0$

Step 4

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

$x - 5 = 0$

$x + 12 = 0$

Step 5

Set $x - 5$ equal to $0$ and solve for $x$ .

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Step 6

Set $x + 12$ equal to $0$ and solve for $x$ .

Set $x + 12$ equal to $0$ .

$x + 12 = 0$

Subtract $12$ from both sides of the equation.

$x = - 12$

Step 7

The final solution is all the values that make $(x - 5) (x + 12) = 0$ true.

$x = 5, - 12$

Solve by Factoring x^2+8x-65=x-5

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