Using a suitable straight line, solve 2x2 - 2x - 1 = 0 given the graph of y = 2x2 - x - 1.

The image is still quite blurry, but I will continue solving the graphing problem (Question 20) from where we left off. I previously solved the first part of the "using a suitable straight line" section. I will now solve the second part, which I will label as (b). Question 20 (continued): Given the graph of y = 2x^2 - x - 1. b) Using a suitable straight line, solve 2x^2 - 2x - 1 = 0. --- b) Solve 2x^2 - 2x - 1 = 0 using the graph of y = 2x^2 - x - 1. Step 1: Identify the given graph equation and the equation to be solved. Given graph: y = 2x^2 - x - 1 Equation to solve: 2x^2 - 2x - 1 = 0 Step 2: Manipulate the equation to be solved to relate it to the given graph equation. We want to express 2x^2 - 2x - 1 = 0 in terms of y = 2x^2 - x - 1. Rewrite 2x^2 - 2x - 1 = 0 as: (2x^2 - x - 1) - x = 0 Substitute y for (2x^2 - x - 1): y - x = 0 y = x This is the equation of the suitable straight line. Step 3: Explain the graphical solution. To solve 2x^2 - 2x - 1 = 0 graphically, you would draw the straight line y = x on the same axes as the graph of y = 2x^2 - x - 1. The solutions for x are the x-coordinates of the points where the straight line intersects the parabola. Step 4: Solve the equation algebraically to find the exact values (as a graph would provide approximations). Using the quadratic formula x = -b ± sqrt(b^2 - 4ac)2a for 2x^2 - 2x - 1 = 0 (where a=2, b=-2, c=-1): x = -(-2) ± sqrt((-2)^2 - 4(2)(-1))2(2) x = 2 ± sqrt(4 + 8)4 x = 2 ± sqrt(12)4 x = 2 ± 2sqrt(3)4 x = 1 ± sqrt(3)2 The solutions are x = 1 + sqrt(3)2 and x = 1 - sqrt(3)2. Approximately, x ≈ (1 + 1.732)/(2) ≈ 1.366 and x ≈ (1 - 1.732)/(2) ≈ -0.366. The suitable straight line is y = x. The solutions are x = 1 ± sqrt(3)2.