x(x-4)=45

Apply the distributive property.

x⋅x+x⋅-4=45

Simplify the expression.

Multiply x by x.

x2+x⋅-4=45

Move -4 to the left of x.

x2-4x=45

x2-4x=45

x2-4x=45

Move 45 to the left side of the equation by subtracting it from both sides.

x2-4x-45=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 -45 and whose sum is -4.

-9,5

Write the factored form using these integers.

(x-9)(x+5)=0

(x-9)(x+5)=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-9=0

x+5=0

Set the first factor equal to 0.

x-9=0

Add 9 to both sides of the equation.

x=9

x=9

Set the next factor equal to 0.

x+5=0

Subtract 5 from both sides of the equation.

x=-5

x=-5

The final solution is all the values that make (x-9)(x+5)=0 true.

x=9,-5

Solve Using the Square Root Property x(x-4)=45