# Solve using the Square Root Property 2y(y+5)=48

2y(y+5)=48
Divide each term by 2 and simplify.
Divide each term in 2y(y+5)=48 by 2.
2y(y+5)2=482
Simplify 2y(y+5)2.
Cancel the common factor of 2.
Cancel the common factor.
2y(y+5)2=482
Divide y(y+5) by 1.
y(y+5)=482
y(y+5)=482
Apply the distributive property.
y⋅y+y⋅5=482
Simplify the expression.
Multiply y by y.
y2+y⋅5=482
Move 5 to the left of y.
y2+5y=482
y2+5y=482
y2+5y=482
Divide 48 by 2.
y2+5y=24
y2+5y=24
Move 24 to the left side of the equation by subtracting it from both sides.
y2+5y-24=0
Factor y2+5y-24 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -24 and whose sum is 5.
-3,8
Write the factored form using these integers.
(y-3)(y+8)=0
(y-3)(y+8)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
y-3=0
y+8=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
y-3=0
Add 3 to both sides of the equation.
y=3
y=3
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
y+8=0
Subtract 8 from both sides of the equation.
y=-8
y=-8
The final solution is all the values that make (y-3)(y+8)=0 true.
y=3,-8
Solve using the Square Root Property 2y(y+5)=48