# Solve Using the Square Root Property 10x^2-21x-10=0 10×2-21x-10=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⋅-10=-100 and whose sum is b=-21.
Factor -21 out of -21x.
10×2-21x-10=0
Rewrite -21 as 4 plus -25
10×2+(4-25)x-10=0
Apply the distributive property.
10×2+4x-25x-10=0
10×2+4x-25x-10=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(10×2+4x)-25x-10=0
Factor out the greatest common factor (GCF) from each group.
2x(5x+2)-5(5x+2)=0
2x(5x+2)-5(5x+2)=0
Factor the polynomial by factoring out the greatest common factor, 5x+2.
(5x+2)(2x-5)=0
(5x+2)(2x-5)=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+2=0
2x-5=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
5x+2=0
Subtract 2 from both sides of the equation.
5x=-2
Divide each term by 5 and simplify.
Divide each term in 5x=-2 by 5.
5×5=-25
Cancel the common factor of 5.
Cancel the common factor.
5×5=-25
Divide x by 1.
x=-25
x=-25
Move the negative in front of the fraction.
x=-25
x=-25
x=-25
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
2x-5=0
Add 5 to both sides of the equation.
2x=5
Divide each term by 2 and simplify.
Divide each term in 2x=5 by 2.
2×2=52
Cancel the common factor of 2.
Cancel the common factor.
2×2=52
Divide x by 1.
x=52
x=52
x=52
x=52
The final solution is all the values that make (5x+2)(2x-5)=0 true.
x=-25,52
Solve Using the Square Root Property 10x^2-21x-10=0     