E. Solve algebraically: V2x -6 + 3 x

find all real solutions of the polynomial equation 6x3+8x2-11x-6=0

To complete the square of x2 + bx, use which of the following?(a) (2b) 2 (b) 2b2 (c) (1/2b)2  (d) 1/2b2

(d) (i) Factorise the quadratic expression x² + 3x - 28. (ii) Use your answer to part (d) (i) to solve the quadratic equation x² + 3x - 28= 0, showing each step in your reasoning. Check that your solution is correct. (e) A student writes down the following piece of work, which contains an error in the reasoning. The equation is: Add 19y to each side: y²-19y=0 y² = 19y y = 19 Divide each side By y: (i) Substitute y = 19 into the left-hand side of the equation y²-19y = 0, and explain why this shows that y = 19 is indeed a solution of the equation. (ii) Write out a complete solution of the equation y2 - 19y = 0. (iii) Explain, as if directly to the student, why their solution is inadequate. (f) Solve the following equation, checking that your solution is correct: 24 72 = 9 <- x+3