Solve by Factoring x^2-10x-75=0

$x^{2} - 10 x - 75 = 0$

Step 1

Factor $x^{2} - 10 x - 75$ 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 $- 75$ and whose sum is $- 10$ .

$- 15, 5$

Write the factored form using these integers.

$(x - 15) (x + 5) = 0$

Step 2

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

$x - 15 = 0$

$x + 5 = 0$

Step 3

Set $x - 15$ equal to $0$ and solve for $x$ .

Set $x - 15$ equal to $0$ .

$x - 15 = 0$

Add $15$ to both sides of the equation.

$x = 15$

Step 4

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

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

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 5

The final solution is all the values that make $(x - 15) (x + 5) = 0$ true.

$x = 15, - 5$

Solve by Factoring x^2-10x-75=0

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