# Solve using the Square Root Property 4x^2+7x-57=0 4×2+7x-57=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=4⋅-57=-228 and whose sum is b=7.
Factor 7 out of 7x.
4×2+7(x)-57=0
Rewrite 7 as -12 plus 19
4×2+(-12+19)x-57=0
Apply the distributive property.
4×2-12x+19x-57=0
4×2-12x+19x-57=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(4×2-12x)+19x-57=0
Factor out the greatest common factor (GCF) from each group.
4x(x-3)+19(x-3)=0
4x(x-3)+19(x-3)=0
Factor the polynomial by factoring out the greatest common factor, x-3.
(x-3)(4x+19)=0
(x-3)(4x+19)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x-3=0
4x+19=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
x-3=0
Add 3 to both sides of the equation.
x=3
x=3
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
4x+19=0
Subtract 19 from both sides of the equation.
4x=-19
Divide each term by 4 and simplify.
Divide each term in 4x=-19 by 4.
4×4=-194
Cancel the common factor of 4.
Cancel the common factor.
4×4=-194
Divide x by 1.
x=-194
x=-194
Move the negative in front of the fraction.
x=-194
x=-194
x=-194
The final solution is all the values that make (x-3)(4x+19)=0 true.
x=3,-194
Solve using the Square Root Property 4x^2+7x-57=0     