# Solve Using the Square Root Property 21x^2=-23x+20

21×2=-23x+20
Add 23x to both sides of the equation.
21×2+23x=20
Move 20 to the left side of the equation by subtracting it from both sides.
21×2+23x-20=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=21⋅-20=-420 and whose sum is b=23.
Factor 23 out of 23x.
21×2+23(x)-20=0
Rewrite 23 as -12 plus 35
21×2+(-12+35)x-20=0
Apply the distributive property.
21×2-12x+35x-20=0
21×2-12x+35x-20=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(21×2-12x)+35x-20=0
Factor out the greatest common factor (GCF) from each group.
3x(7x-4)+5(7x-4)=0
3x(7x-4)+5(7x-4)=0
Factor the polynomial by factoring out the greatest common factor, 7x-4.
(7x-4)(3x+5)=0
(7x-4)(3x+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.
7x-4=0
3x+5=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
7x-4=0
Add 4 to both sides of the equation.
7x=4
Divide each term by 7 and simplify.
Divide each term in 7x=4 by 7.
7×7=47
Cancel the common factor of 7.
Cancel the common factor.
7×7=47
Divide x by 1.
x=47
x=47
x=47
x=47
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
3x+5=0
Subtract 5 from both sides of the equation.
3x=-5
Divide each term by 3 and simplify.
Divide each term in 3x=-5 by 3.
3×3=-53
Cancel the common factor of 3.
Cancel the common factor.
3×3=-53
Divide x by 1.
x=-53
x=-53
Move the negative in front of the fraction.
x=-53
x=-53
x=-53
The final solution is all the values that make (7x-4)(3x+5)=0 true.
x=47,-53
Solve Using the Square Root Property 21x^2=-23x+20

Scroll to top