# Solve Using the Square Root Property 10x^2-x-3=0 10×2-x-3=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=10⋅-3=-30 and whose sum is b=-1.
Factor -1 out of -x.
10×2-(x)-3=0
Rewrite -1 as 5 plus -6
10×2+(5-6)x-3=0
Apply the distributive property.
10×2+5x-6x-3=0
10×2+5x-6x-3=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(10×2+5x)-6x-3=0
Factor out the greatest common factor (GCF) from each group.
5x(2x+1)-3(2x+1)=0
5x(2x+1)-3(2x+1)=0
Factor the polynomial by factoring out the greatest common factor, 2x+1.
(2x+1)(5x-3)=0
(2x+1)(5x-3)=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
5x-3=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.
5x-3=0
Add 3 to both sides of the equation.
5x=3
Divide each term by 5 and simplify.
Divide each term in 5x=3 by 5.
5×5=35
Cancel the common factor of 5.
Cancel the common factor.
5×5=35
Divide x by 1.
x=35
x=35
x=35
x=35
The final solution is all the values that make (2x+1)(5x-3)=0 true.
x=-12,35
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