Solve by Factoring x^2=9x+10

$x^{2} = 9 x + 10$

Step 1

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

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

$x^{2} - 9 x = 10$

Subtract $10$ from both sides of the equation.

$x^{2} - 9 x - 10 = 0$

Step 2

Factor $x^{2} - 9 x - 10$ 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 $- 10$ and whose sum is $- 9$ .

$- 10, 1$

Write the factored form using these integers.

$(x - 10) (x + 1) = 0$

Step 3

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

$x - 10 = 0$

$x + 1 = 0$

Step 4

Set $x - 10$ equal to $0$ and solve for $x$ .

Set $x - 10$ equal to $0$ .

$x - 10 = 0$

Add $10$ to both sides of the equation.

$x = 10$

Step 5

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 6

The final solution is all the values that make $(x - 10) (x + 1) = 0$ true.

$x = 10, - 1$

Solve by Factoring x^2=9x+10

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