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

4×2-14x-8=0
Factor the left side of the equation.
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 by 2 and simplify.
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
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
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.
2×2-7x-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 and solve.
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 and solve.
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