use the quadratic formula to solve the quadratic equation 10x^2 +5x=5x-8. express its solution in the form a+-bi

Answer 1

To solve the quadratic equation 10x^2 + 5x = 5x - 8 using the quadratic formula, we start by setting the equation equal to zero:

10x^2 + 5x - 5x + 8 = 0

Simplifying:

10x^2 + 8 = 0

Now, we can use the quadratic formula, which states that for any equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values from our equation:

a = 10, b = 0, c = 8

x = (-(0) ± √((0)^2 - 4(10)(8))) / (2(10))

Simplifying further:

x = ± √(-320) / 20

x = ± √(-16) / 2

x = ± (4i) / 2

Finally, expressing the solution in the form a ± bi:

x = ± 2i