Question

Solve the equation for x, where x is a real number:
-4x^2 + 5x - 7 = 0

Answer 1

To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
x = [ -b ± √(b^2 - 4ac) ] / (2a)
x = [ -5 ± √((5)^2 - 4(-4)(-7)) ] / ( 2(-4) )
x = [-5 ± √(25 - (112) ) ] / ( -8 )
x = [-5 ± √(-87) ] / ( -8)
Since √-87 is nonreal, there are no real solutions to the given equation.

Answer 2

The equation has no real solutions. (There are no x-intercepts.)

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The complex solutions are x = 0.625 ±i√1.359375