# Solve Using the Square Root Property 15x^2+2x-1=0 15×2+2x-1=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=15⋅-1=-15 and whose sum is b=2.
Factor 2 out of 2x.
15×2+2(x)-1=0
Rewrite 2 as -3 plus 5
15×2+(-3+5)x-1=0
Apply the distributive property.
15×2-3x+5x-1=0
15×2-3x+5x-1=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(15×2-3x)+5x-1=0
Factor out the greatest common factor (GCF) from each group.
3x(5x-1)+1(5x-1)=0
3x(5x-1)+1(5x-1)=0
Factor the polynomial by factoring out the greatest common factor, 5x-1.
(5x-1)(3x+1)=0
(5x-1)(3x+1)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
5x-1=0
3x+1=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
5x-1=0
Add 1 to both sides of the equation.
5x=1
Divide each term by 5 and simplify.
Divide each term in 5x=1 by 5.
5×5=15
Cancel the common factor of 5.
Cancel the common factor.
5×5=15
Divide x by 1.
x=15
x=15
x=15
x=15
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
3x+1=0
Subtract 1 from both sides of the equation.
3x=-1
Divide each term by 3 and simplify.
Divide each term in 3x=-1 by 3.
3×3=-13
Cancel the common factor of 3.
Cancel the common factor.
3×3=-13
Divide x by 1.
x=-13
x=-13
Move the negative in front of the fraction.
x=-13
x=-13
x=-13
The final solution is all the values that make (5x-1)(3x+1)=0 true.
x=15,-13
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