# Solve Using the Square Root Property 2x^2-2x-4=0 2×2-2x-4=0
Factor the left side of the equation.
Factor 2 out of 2×2-2x-4.
Factor 2 out of 2×2.
2(x2)-2x-4=0
Factor 2 out of -2x.
2(x2)+2(-x)-4=0
Factor 2 out of -4.
2(x2)+2(-x)+2(-2)=0
Factor 2 out of 2(x2)+2(-x).
2(x2-x)+2(-2)=0
Factor 2 out of 2(x2-x)+2(-2).
2(x2-x-2)=0
2(x2-x-2)=0
Factor.
Factor x2-x-2 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 -2 and whose sum is -1.
-2,1
Write the factored form using these integers.
2((x-2)(x+1))=0
2((x-2)(x+1))=0
Remove unnecessary parentheses.
2(x-2)(x+1)=0
2(x-2)(x+1)=0
2(x-2)(x+1)=0
Divide each term by 2 and simplify.
Divide each term in 2(x-2)(x+1)=0 by 2.
2(x-2)(x+1)2=02
Simplify 2(x-2)(x+1)2.
Cancel the common factor of 2.
Cancel the common factor.
2(x-2)(x+1)2=02
Divide (x-2)(x+1) by 1.
(x-2)(x+1)=02
(x-2)(x+1)=02
Expand (x-2)(x+1) using the FOIL Method.
Apply the distributive property.
x(x+1)-2(x+1)=02
Apply the distributive property.
x⋅x+x⋅1-2(x+1)=02
Apply the distributive property.
x⋅x+x⋅1-2x-2⋅1=02
x⋅x+x⋅1-2x-2⋅1=02
Simplify and combine like terms.
Simplify each term.
Multiply x by x.
x2+x⋅1-2x-2⋅1=02
Multiply x by 1.
x2+x-2x-2⋅1=02
Multiply -2 by 1.
x2+x-2x-2=02
x2+x-2x-2=02
Subtract 2x from x.
x2-x-2=02
x2-x-2=02
x2-x-2=02
Divide 0 by 2.
x2-x-2=0
x2-x-2=0
Factor x2-x-2 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 -2 and whose sum is -1.
-2,1
Write the factored form using these integers.
(x-2)(x+1)=0
(x-2)(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-2=0
x+1=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+1=0
Subtract 1 from both sides of the equation.
x=-1
x=-1
The final solution is all the values that make (x-2)(x+1)=0 true.
x=2,-1
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