Answer:
x = 5, x = 1
Explanation:
The quadratic equation 0 = 4(x - 3)2 - 16.
Using binomial theorem, (a - b)2 = a2 - 2ab + b2 to expand (x - 3)2.
0 = 4(x2 - 6x + 9 ) - 16.
Using distributive property to multiply 4 by x2 - 6x + 9.
0 = 4x2 - 24x + 36 - 16.
Subtract 16 from 36 to get 20.
0 = 4x2 - 24x + 20.
4x2 - 24x + 20 = 0.
Divide both sides by 4.
x2 - 6x + 5 = 0.
To solve the equation, factor and rewrite as x2 + ax + bx + 5
a + b = -6, ab = 1(5) = 5.
a = -5, b = -1.
Rewriting x2 - 6x + 5 as
(x2 - 5x) + (-x + 5)
Factor x in the first and -1 in the second group.
x(x - 5) - (x - 5)
Factor out common term
(x - 5)(x - 1)
By solving the above, we get
x = 5, x = 1