Expanding the left side of the equation:
(3x-1)(2x-2)= 3x(2x) +3x(-2) -1(2x) -1(-2)= 6x^2 - 6x - 2x + 2= 6x^2 - 8x + 2
Expanding the right side of the equation:
(x-4)^2 + 7= (x-4)(x-4) + 7= x(x) -4(x) -4(x) + 4(4) + 7= x^2 - 4x - 4x + 16 + 7= x^2 - 8x + 23
Setting the two sides equal to each other:
6x^2 - 8x + 2 = x^2 - 8x + 23Subtract x^2 and -8x from both sides:5x^2 + 10 = 23Subtracting 10 from both sides:5x^2 = 13Dividing by 5:x^2 = 13/5Taking square root of both sides:x = ±√(13/5)
Therefore, the solutions are:x = √(13/5) and x = -√(13/5)
Expanding the left side of the equation:
(3x-1)(2x-2)
= 3x(2x) +3x(-2) -1(2x) -1(-2)
= 6x^2 - 6x - 2x + 2
= 6x^2 - 8x + 2
Expanding the right side of the equation:
(x-4)^2 + 7
= (x-4)(x-4) + 7
= x(x) -4(x) -4(x) + 4(4) + 7
= x^2 - 4x - 4x + 16 + 7
= x^2 - 8x + 23
Setting the two sides equal to each other:
6x^2 - 8x + 2 = x^2 - 8x + 23
Subtract x^2 and -8x from both sides:
5x^2 + 10 = 23
Subtracting 10 from both sides:
5x^2 = 13
Dividing by 5:
x^2 = 13/5
Taking square root of both sides:
x = ±√(13/5)
Therefore, the solutions are:
x = √(13/5) and x = -√(13/5)