Solve Using the Square Root Property 232=(3x+5)(x)

232=(3x+5)(x)
Rewrite the equation as (3x+5)(x)=232.
(3x+5)(x)=232
Simplify (3x+5)(x).
Apply the distributive property.
3x⋅x+5x=232
Multiply x by x by adding the exponents.
Move x.
3(x⋅x)+5x=232
Multiply x by x.
3×2+5x=232
3×2+5x=232
3×2+5x=232
Move 232 to the left side of the equation by subtracting it from both sides.
3×2+5x-232=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=3⋅-232=-696 and whose sum is b=5.
Factor 5 out of 5x.
3×2+5(x)-232=0
Rewrite 5 as -24 plus 29
3×2+(-24+29)x-232=0
Apply the distributive property.
3×2-24x+29x-232=0
3×2-24x+29x-232=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(3×2-24x)+29x-232=0
Factor out the greatest common factor (GCF) from each group.
3x(x-8)+29(x-8)=0
3x(x-8)+29(x-8)=0
Factor the polynomial by factoring out the greatest common factor, x-8.
(x-8)(3x+29)=0
(x-8)(3x+29)=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-8=0
3x+29=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
x-8=0
Add 8 to both sides of the equation.
x=8
x=8
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
3x+29=0
Subtract 29 from both sides of the equation.
3x=-29
Divide each term by 3 and simplify.
Divide each term in 3x=-29 by 3.
3×3=-293
Cancel the common factor of 3.
Cancel the common factor.
3×3=-293
Divide x by 1.
x=-293
x=-293
Move the negative in front of the fraction.
x=-293
x=-293
x=-293
The final solution is all the values that make (x-8)(3x+29)=0 true.
x=8,-293
Solve Using the Square Root Property 232=(3x+5)(x)