# Solve Using the Square Root Property 2x(x+1)=12 2x(x+1)=12
Divide each term by 2 and simplify.
Divide each term in 2x(x+1)=12 by 2.
2x(x+1)2=122
Simplify 2x(x+1)2.
Cancel the common factor of 2.
Cancel the common factor.
2x(x+1)2=122
Divide x(x+1) by 1.
x(x+1)=122
x(x+1)=122
Apply the distributive property.
x⋅x+x⋅1=122
Simplify the expression.
Multiply x by x.
x2+x⋅1=122
Multiply x by 1.
x2+x=122
x2+x=122
x2+x=122
Divide 12 by 2.
x2+x=6
x2+x=6
Move 6 to the left side of the equation by subtracting it from both sides.
x2+x-6=0
Factor x2+x-6 using the AC method.
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 -6 and whose sum is 1.
-2,3
Write the factored form using these integers.
(x-2)(x+3)=0
(x-2)(x+3)=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-2=0
x+3=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
x-2=0
Add 2 to both sides of the equation.
x=2
x=2
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
x+3=0
Subtract 3 from both sides of the equation.
x=-3
x=-3
The final solution is all the values that make (x-2)(x+3)=0 true.
x=2,-3
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