2×2-2x-4=0

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 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

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.

x-2=0

Add 2 to both sides of the equation.

x=2

x=2

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

Solve Using the Square Root Property 2x^2-2x-4=0