4×2-18x-52=0

Factor 2 out of 4×2-18x-52.

Factor 2 out of 4×2.

2(2×2)-18x-52=0

Factor 2 out of -18x.

2(2×2)+2(-9x)-52=0

Factor 2 out of -52.

2(2×2)+2(-9x)+2(-26)=0

Factor 2 out of 2(2×2)+2(-9x).

2(2×2-9x)+2(-26)=0

Factor 2 out of 2(2×2-9x)+2(-26).

2(2×2-9x-26)=0

2(2×2-9x-26)=0

Factor.

Factor by grouping.

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅-26=-52 and whose sum is b=-9.

Factor -9 out of -9x.

2(2×2-9x-26)=0

Rewrite -9 as 4 plus -13

2(2×2+(4-13)x-26)=0

Apply the distributive property.

2(2×2+4x-13x-26)=0

2(2×2+4x-13x-26)=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

2((2×2+4x)-13x-26)=0

Factor out the greatest common factor (GCF) from each group.

2(2x(x+2)-13(x+2))=0

2(2x(x+2)-13(x+2))=0

Factor the polynomial by factoring out the greatest common factor, x+2.

2((x+2)(2x-13))=0

2((x+2)(2x-13))=0

Remove unnecessary parentheses.

2(x+2)(2x-13)=0

2(x+2)(2x-13)=0

2(x+2)(2x-13)=0

Divide each term in 2(x+2)(2x-13)=0 by 2.

2(x+2)(2x-13)2=02

Simplify 2(x+2)(2x-13)2.

Cancel the common factor of 2.

Cancel the common factor.

2(x+2)(2x-13)2=02

Divide (x+2)(2x-13) by 1.

(x+2)(2x-13)=02

(x+2)(2x-13)=02

Expand (x+2)(2x-13) using the FOIL Method.

Apply the distributive property.

x(2x-13)+2(2x-13)=02

Apply the distributive property.

x(2x)+x⋅-13+2(2x-13)=02

Apply the distributive property.

x(2x)+x⋅-13+2(2x)+2⋅-13=02

x(2x)+x⋅-13+2(2x)+2⋅-13=02

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

2x⋅x+x⋅-13+2(2x)+2⋅-13=02

Multiply x by x by adding the exponents.

Move x.

2(x⋅x)+x⋅-13+2(2x)+2⋅-13=02

Multiply x by x.

2×2+x⋅-13+2(2x)+2⋅-13=02

2×2+x⋅-13+2(2x)+2⋅-13=02

Move -13 to the left of x.

2×2-13⋅x+2(2x)+2⋅-13=02

Multiply 2 by 2.

2×2-13x+4x+2⋅-13=02

Multiply 2 by -13.

2×2-13x+4x-26=02

2×2-13x+4x-26=02

Add -13x and 4x.

2×2-9x-26=02

2×2-9x-26=02

2×2-9x-26=02

Divide 0 by 2.

2×2-9x-26=0

2×2-9x-26=0

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅-26=-52 and whose sum is b=-9.

Factor -9 out of -9x.

2×2-9x-26=0

Rewrite -9 as 4 plus -13

2×2+(4-13)x-26=0

Apply the distributive property.

2×2+4x-13x-26=0

2×2+4x-13x-26=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(2×2+4x)-13x-26=0

Factor out the greatest common factor (GCF) from each group.

2x(x+2)-13(x+2)=0

2x(x+2)-13(x+2)=0

Factor the polynomial by factoring out the greatest common factor, x+2.

(x+2)(2x-13)=0

(x+2)(2x-13)=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

2x-13=0

Set the first factor equal to 0.

x+2=0

Subtract 2 from both sides of the equation.

x=-2

x=-2

Set the next factor equal to 0.

2x-13=0

Add 13 to both sides of the equation.

2x=13

Divide each term by 2 and simplify.

Divide each term in 2x=13 by 2.

2×2=132

Cancel the common factor of 2.

Cancel the common factor.

2×2=132

Divide x by 1.

x=132

x=132

x=132

x=132

The final solution is all the values that make (x+2)(2x-13)=0 true.

x=-2,132

Solve Using the Square Root Property 4x^2-18x-52=0