x2-x=42

Move 42 to the left side of the equation by subtracting it from both sides.

x2-x-42=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 -42 and whose sum is -1.

-7,6

Write the factored form using these integers.

(x-7)(x+6)=0

(x-7)(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-7=0

x+6=0

Set the first factor equal to 0.

x-7=0

Add 7 to both sides of the equation.

x=7

x=7

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-7)(x+6)=0 true.

x=7,-6

Solve using the Square Root Property x^2-x=42