4×2-14x-8=0

Factor 2 out of 4×2-14x-8.

Factor 2 out of 4×2.

2(2×2)-14x-8=0

Factor 2 out of -14x.

2(2×2)+2(-7x)-8=0

Factor 2 out of -8.

2(2×2)+2(-7x)+2(-4)=0

Factor 2 out of 2(2×2)+2(-7x).

2(2×2-7x)+2(-4)=0

Factor 2 out of 2(2×2-7x)+2(-4).

2(2×2-7x-4)=0

2(2×2-7x-4)=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⋅-4=-8 and whose sum is b=-7.

Factor -7 out of -7x.

2(2×2-7x-4)=0

Rewrite -7 as 1 plus -8

2(2×2+(1-8)x-4)=0

Apply the distributive property.

2(2×2+1x-8x-4)=0

Multiply x by 1.

2(2×2+x-8x-4)=0

2(2×2+x-8x-4)=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

2((2×2+x)-8x-4)=0

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

2(x(2x+1)-4(2x+1))=0

2(x(2x+1)-4(2x+1))=0

Factor the polynomial by factoring out the greatest common factor, 2x+1.

2((2x+1)(x-4))=0

2((2x+1)(x-4))=0

Remove unnecessary parentheses.

2(2x+1)(x-4)=0

2(2x+1)(x-4)=0

2(2x+1)(x-4)=0

Divide each term in 2(2x+1)(x-4)=0 by 2.

2(2x+1)(x-4)2=02

Simplify 2(2x+1)(x-4)2.

Cancel the common factor of 2.

Cancel the common factor.

2(2x+1)(x-4)2=02

Divide (2x+1)(x-4) by 1.

(2x+1)(x-4)=02

(2x+1)(x-4)=02

Expand (2x+1)(x-4) using the FOIL Method.

Apply the distributive property.

2x(x-4)+1(x-4)=02

Apply the distributive property.

2x⋅x+2x⋅-4+1(x-4)=02

Apply the distributive property.

2x⋅x+2x⋅-4+1x+1⋅-4=02

2x⋅x+2x⋅-4+1x+1⋅-4=02

Simplify and combine like terms.

Simplify each term.

Multiply x by x by adding the exponents.

Move x.

2(x⋅x)+2x⋅-4+1x+1⋅-4=02

Multiply x by x.

2×2+2x⋅-4+1x+1⋅-4=02

2×2+2x⋅-4+1x+1⋅-4=02

Multiply -4 by 2.

2×2-8x+1x+1⋅-4=02

Multiply x by 1.

2×2-8x+x+1⋅-4=02

Multiply -4 by 1.

2×2-8x+x-4=02

2×2-8x+x-4=02

Add -8x and x.

2×2-7x-4=02

2×2-7x-4=02

2×2-7x-4=02

Divide 0 by 2.

2×2-7x-4=0

2×2-7x-4=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⋅-4=-8 and whose sum is b=-7.

Factor -7 out of -7x.

2×2-7x-4=0

Rewrite -7 as 1 plus -8

2×2+(1-8)x-4=0

Apply the distributive property.

2×2+1x-8x-4=0

Multiply x by 1.

2×2+x-8x-4=0

2×2+x-8x-4=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(2×2+x)-8x-4=0

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

x(2x+1)-4(2x+1)=0

x(2x+1)-4(2x+1)=0

Factor the polynomial by factoring out the greatest common factor, 2x+1.

(2x+1)(x-4)=0

(2x+1)(x-4)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

2x+1=0

x-4=0

Set the first factor equal to 0.

2x+1=0

Subtract 1 from both sides of the equation.

2x=-1

Divide each term by 2 and simplify.

Divide each term in 2x=-1 by 2.

2×2=-12

Cancel the common factor of 2.

Cancel the common factor.

2×2=-12

Divide x by 1.

x=-12

x=-12

Move the negative in front of the fraction.

x=-12

x=-12

x=-12

Set the next factor equal to 0.

x-4=0

Add 4 to both sides of the equation.

x=4

x=4

The final solution is all the values that make (2x+1)(x-4)=0 true.

x=-12,4

Solve Using the Square Root Property 4x^2-14x-8=0