Using the quadratic formula to solve 2x² = 4x – 7, what are the values of x?

The quadratic formula is the easiest way of solving quadratic equations especially when the splitting of the middle term is not feasible.

Answer: x =  (2 ± √10 i)/2 are the solutions of the quadratic equation 2x² = 4x - 7

Let us use the quadratic formula to solve 2x² = 4x – 7.

Explanation:

Let's write the equation in its standard form.

2x² = 4x – 7

2x² - 4x + 7 = 0

a = 2, b = -4, c = 7          ------->   when we compare with the standard form of a quadratic expression ax² + bx + c = 0

By quadratic formula,

x = [ -b ± √(b² - 4ac) ] / 2a

x =  [ -(-4) ± √{(-4)² - 4(2)(7)} ] / 2(2)

x =  [ 4 ± √{16 - 56} ] / 4

x =  [ 4 ± √(-40) ] / 4

x =  [ 4 ± 2√10 i ] / 4

x =  (2 ± √10i)/2

values of x are : (2 + √10 i)/2   and  (2 - √10 i)/2

Both the values of x are complex numbers.

Thus, we have seen the solutions of the quadratic expression 2x² = 4x – 7, using the quadratic formula.