x 32 3x2 5x 12SolutionWe have x 32 3x2 5x 12 or x2

Solution

We have ( x - 3)² + 3x² - 5x = 12 or, x² - 6x + 9 + 3x² - 5x = 12 or, 4x² - 11x - 3 = 0 or, 4x² - 12x + x - 3 = 0 or, 4x(x -3) + 1 (x -3 ) = 0 or, ( x - 3)( 4x + 1) = 0 . Therefore, either x - 3 = 0 which means that x = 3 or, 4x + 1 = 0 which means that x = - 1/4. Thus, the answer is that either x = 3 or, x = -1/4. We can verify this by substituting these values of x in the original equation.