# Solve Using the Square Root Property 24x^2-5x-36=0 24×2-5x-36=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=24⋅-36=-864 and whose sum is b=-5.
Factor -5 out of -5x.
24×2-5x-36=0
Rewrite -5 as 27 plus -32
24×2+(27-32)x-36=0
Apply the distributive property.
24×2+27x-32x-36=0
24×2+27x-32x-36=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(24×2+27x)-32x-36=0
Factor out the greatest common factor (GCF) from each group.
3x(8x+9)-4(8x+9)=0
3x(8x+9)-4(8x+9)=0
Factor the polynomial by factoring out the greatest common factor, 8x+9.
(8x+9)(3x-4)=0
(8x+9)(3x-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.
8x+9=0
3x-4=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
8x+9=0
Subtract 9 from both sides of the equation.
8x=-9
Divide each term by 8 and simplify.
Divide each term in 8x=-9 by 8.
8×8=-98
Cancel the common factor of 8.
Cancel the common factor.
8×8=-98
Divide x by 1.
x=-98
x=-98
Move the negative in front of the fraction.
x=-98
x=-98
x=-98
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
3x-4=0
Add 4 to both sides of the equation.
3x=4
Divide each term by 3 and simplify.
Divide each term in 3x=4 by 3.
3×3=43
Cancel the common factor of 3.
Cancel the common factor.
3×3=43
Divide x by 1.
x=43
x=43
x=43
x=43
The final solution is all the values that make (8x+9)(3x-4)=0 true.
x=-98,43
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