# Solve Using the Square Root Property 10x^2-4=3x 10×2-4=3x
Subtract 3x from both sides of the equation.
10×2-4-3x=0
Factor by grouping.
Reorder terms.
10×2-3x-4=0
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⋅-4=-40 and whose sum is b=-3.
Factor -3 out of -3x.
10×2-3x-4=0
Rewrite -3 as 5 plus -8
10×2+(5-8)x-4=0
Apply the distributive property.
10×2+5x-8x-4=0
10×2+5x-8x-4=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(10×2+5x)-8x-4=0
Factor out the greatest common factor (GCF) from each group.
5x(2x+1)-4(2x+1)=0
5x(2x+1)-4(2x+1)=0
Factor the polynomial by factoring out the greatest common factor, 2x+1.
(2x+1)(5x-4)=0
(2x+1)(5x-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.
2x+1=0
5x-4=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-4=0
Add 4 to both sides of the equation.
5x=4
Divide each term by 5 and simplify.
Divide each term in 5x=4 by 5.
5×5=45
Cancel the common factor of 5.
Cancel the common factor.
5×5=45
Divide x by 1.
x=45
x=45
x=45
x=45
The final solution is all the values that make (2x+1)(5x-4)=0 true.
x=-12,45
Solve Using the Square Root Property 10x^2-4=3x     