Question

Using the quadratic formula to solve 2x^2 = 4x – 7, what are the values of x?

Answer 1

Answer:

Step-by-step explanation:

To use the quadratic formula, we must write the quadratic in standard form, viz:

2x^2 - 4x + 7 = 0

Start by calculating the discriminant.  That's b^2 - 4(a)(c).  Here,

a = 2, b = -4 and c = 7, and so the discriminant for this particular problem is

(-4)^2 - 4(2)(7), or 16 - 56, or 40.

Recall that  a positive discriminant indicates two real, unequal roots.

Now we write out the whole quadratic formula, with the appropriate constants inserted (see above):

       -(-4) ± √40          4 ± (√4)(√10)          4 ± 2√10

x = --------------------- = ----------------------  =  ---------------

               2(2)                        4                          4

                                    2 ± √10

which reduces to x = --------------

                                          2