x(x-11)=12

Apply the distributive property.

x⋅x+x⋅-11=12

Simplify the expression.

Multiply x by x.

x2+x⋅-11=12

Move -11 to the left of x.

x2-11x=12

x2-11x=12

x2-11x=12

Move 12 to the left side of the equation by subtracting it from both sides.

x2-11x-12=0

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -12 and whose sum is -11.

-12,1

Write the factored form using these integers.

(x-12)(x+1)=0

(x-12)(x+1)=0

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

x-12=0

x+1=0

Set the first factor equal to 0.

x-12=0

Add 12 to both sides of the equation.

x=12

x=12

Set the next factor equal to 0.

x+1=0

Subtract 1 from both sides of the equation.

x=-1

x=-1

The final solution is all the values that make (x-12)(x+1)=0 true.

x=12,-1

Solve Using the Square Root Property x(x-11)=12