Solve 2x² = 4x - 7 using the quadratic formula?

Solution:

Given that:

2x² = 4x - 7 

It can be written as in arranged form as :

2x² - 4x + 7 = 0

The formula for the standard form of quadratic equation ax² + bx + c = 0 is written as

x = [−b ± √(b² − 4ac)] / 2a

From the given equation we know that

a = 2

b = -4

c = 7

Substituting it in the formula

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

x = [ 4 ± √{16 - 56} ] / 4

By further calculation

x = [ 4 ± √(-40) ] / 4

x = [ 4 ± 2√10 i ] / 4

x = (2 ± √10i)/2

Therefore, the values of x are (2 + √10 i)/2 and (2 - √10 i)/2.

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Solve 2x² = 4x - 7 using the quadratic formula?

Summary:

By solving 2x² = 4x - 7 using the quadratic formula, the values of x are (2 + √10 i)/2 and (2 - √10 i)/2.