16x2 + 8x + 1 = 0 : This factorises to (4x + 1)(4x + 1) = 0 When 4x + 1 = 0 then 4x = -1 : x = -1/4.
16x2 - 56x + 49 = (4x - 7)2
16x2 + 32x - 65 = 0 factorises (4x + 13)(4x - 5) This makes x either -13/4 or 5/4.
This is an example of a quadratic equation. It has many solutions depending of the value of x. Its solution would commonly be shown as a graph. For example, if x = 2 then the answer is 22 + 16x2 +55 = 4+32+55 = 91. if x = 3 then the answer is 32 + 16x3 + 55 = 9+48+55 = 112. [but check my arithmetic!]
(4x + 6)(4x - 6)
16x2 - 49 = 42x2 - 72 = (4x)2 - 72 = (4x - 7)(4x + 7)
4x times 4x equals 16x2.
Equals means=ok
10x2 - 56 = 88 - 6x2 : 10x2 + 6x2 = 88 + 56 : 16x2 = 144 : x2 = 9 : x = ± 3
sqrt(10x)*sqrt(8x) = sqrt(80x2) = sqrt(16x2*5) = sqrt(16x2)*sqrt(5) = 4x*sqrt(5)
If you can't factor it easily, use the quadratic formula.
16x2 + 8x + 1 = 0 : This factorises to (4x + 1)(4x + 1) = 0 When 4x + 1 = 0 then 4x = -1 : x = -1/4.
Calculate 10^2 - 4*(-16)*(-20)
4X = 16X2 4X - 16X2 = 0 (1 - 4X)4X = 0 ------------------ as you see X = 0 -------- 1 - 4X = 0 - 4X = - 1 X = 1/4 ----------- So, X = 0 and X = 1/4. You check.
The derivative of y=arcsin(4x) is dy/dx = 4/sqrt(1-16x2).
It is: 4-16x2 = (2-4x)(2+4x) when factored
You double the product of 2x8.2x8 equals 16. 16 doubled which equal 16x2 equals 32.4x8 equals 32.