x(x-5)=66

Apply the distributive property.

x⋅x+x⋅-5=66

Simplify the expression.

Multiply x by x.

x2+x⋅-5=66

Move -5 to the left of x.

x2-5x=66

x2-5x=66

x2-5x=66

Move 66 to the left side of the equation by subtracting it from both sides.

x2-5x-66=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 -66 and whose sum is -5.

-11,6

Write the factored form using these integers.

(x-11)(x+6)=0

(x-11)(x+6)=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-11=0

x+6=0

Set the first factor equal to 0.

x-11=0

Add 11 to both sides of the equation.

x=11

x=11

Set the next factor equal to 0.

x+6=0

Subtract 6 from both sides of the equation.

x=-6

x=-6

The final solution is all the values that make (x-11)(x+6)=0 true.

x=11,-6

Solve Using the Square Root Property x(x-5)=66