Use the substitution method (explained in Exercise) to solve the quadratic equation 2x2 −...

Use the substitution method (explained in Exercise) to solve the quadratic equation 2x2 − 3x + 1 = 0.

Exercise

We solved quadratic equations by factoring and by using the quadratic formula. This exercise shows how to solve a quadratic equation by the method of substitution. As an example, we use the equation

(a) In equation (1), make the substitution x = y + k. Show that the resulting equation can be written

(b) Find a value for k so that the coefficient of y in equation (2) is 0. Then, using this value of k, show that equation (2) becomes y2 = 5/4.

(c) Solve the equation y2 = 5/4. Then use the equation x = y + k to obtain the solutions of equation (1).