Solve Using the Square Root Property 16x-16=4x^2

16x-16=4×2
Subtract 4×2 from both sides of the equation.
16x-16-4×2=0
Factor the left side of the equation.
Factor -4 out of 16x-16-4×2.
Reorder the expression.
Move -16.
16x-4×2-16=0
Reorder 16x and -4×2.
-4×2+16x-16=0
-4×2+16x-16=0
Factor -4 out of -4×2.
-4×2+16x-16=0
Factor -4 out of 16x.
-4×2-4(-4x)-16=0
Factor -4 out of -16.
-4×2-4(-4x)-4⋅4=0
Factor -4 out of -4(x2)-4(-4x).
-4(x2-4x)-4⋅4=0
Factor -4 out of -4(x2-4x)-4(4).
-4(x2-4x+4)=0
-4(x2-4x+4)=0
Factor using the perfect square rule.
Rewrite 4 as 22.
-4(x2-4x+22)=0
Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.
2ab=2⋅x⋅-2
Simplify.
2ab=-4x
Factor using the perfect square trinomial rule a2-2ab+b2=(a-b)2, where a=x and b=-2.
-4(x-2)2=0
-4(x-2)2=0
-4(x-2)2=0
Divide each term by -4 and simplify.
Divide each term in -4(x-2)2=0 by -4.
-4(x-2)2-4=0-4
Cancel the common factor of -4.
Cancel the common factor.
-4(x-2)2-4=0-4
Divide (x-2)2 by 1.
(x-2)2=0-4
(x-2)2=0-4
Divide 0 by -4.
(x-2)2=0
(x-2)2=0
Set the x-2 equal to 0.
x-2=0
Add 2 to both sides of the equation.
x=2
Solve Using the Square Root Property 16x-16=4x^2