1) 12x^2 - 25 = 12x^2 = 2x^2 = 25/1x = ±√(25/12x = ±(5/√12x = ±(5√3)/6
2) (x - 1)^2 + 3 = (x - 1)^2 = -There are no real solutions for this equation because a square of a real number cannot be negative.
3) √16x^2 - 24x + 9 = 14x - 24x + 9 = 14x^2 - 24x - 2 = 2(2x^2 - 12x - 1) = Using the quadratic formula, we findx = (12 ± √(12^2 + 8))/x = (12 ± √(144 + 8))/x = (12 ± √152)/x = (12 ± 2√38)/x = 3 ± √38/2
So, the solutions are x = 3 + √38/2 or x = 3 - √38/2.
1) 12x^2 - 25 =
12x^2 = 2
x^2 = 25/1
x = ±√(25/12
x = ±(5/√12
x = ±(5√3)/6
2) (x - 1)^2 + 3 =
(x - 1)^2 = -
There are no real solutions for this equation because a square of a real number cannot be negative.
3) √16x^2 - 24x + 9 = 1
4x - 24x + 9 = 1
4x^2 - 24x - 2 =
2(2x^2 - 12x - 1) =
Using the quadratic formula, we find
x = (12 ± √(12^2 + 8))/
x = (12 ± √(144 + 8))/
x = (12 ± √152)/
x = (12 ± 2√38)/
x = 3 ± √38/2
So, the solutions are x = 3 + √38/2 or x = 3 - √38/2.