# Solve Using the Square Root Property 6x^2-13x-8=0 6×2-13x-8=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=6⋅-8=-48 and whose sum is b=-13.
Factor -13 out of -13x.
6×2-13x-8=0
Rewrite -13 as 3 plus -16
6×2+(3-16)x-8=0
Apply the distributive property.
6×2+3x-16x-8=0
6×2+3x-16x-8=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(6×2+3x)-16x-8=0
Factor out the greatest common factor (GCF) from each group.
3x(2x+1)-8(2x+1)=0
3x(2x+1)-8(2x+1)=0
Factor the polynomial by factoring out the greatest common factor, 2x+1.
(2x+1)(3x-8)=0
(2x+1)(3x-8)=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
3x-8=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.
3x-8=0
Add 8 to both sides of the equation.
3x=8
Divide each term by 3 and simplify.
Divide each term in 3x=8 by 3.
3×3=83
Cancel the common factor of 3.
Cancel the common factor.
3×3=83
Divide x by 1.
x=83
x=83
x=83
x=83
The final solution is all the values that make (2x+1)(3x-8)=0 true.
x=-12,83
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