y = -16x2 + 342
At the x-intercepts, y=0
-16x2 + 342 = 0
16x2 = 342
x2 = 342/16 = 21.375
x = plus and minus sqrt(21.375) = approx. plus and minus 4.6233 (rounded)
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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)