which of the following is a solution to the quadratic equation 2x^2-5x=6? assume that the solution has been rounded to the nearest hundredth if applicable.

Question

x=0.89

x=1.03

x=-0.89

x=-1.03

Answer 1

To find the solutions to the quadratic equation, we can set the equation equal to zero:

2x^2 - 5x = 6

Rearranging the terms:

2x^2 - 5x - 6 = 0

To find the solutions, we can factor or use the quadratic formula. In this case, factoring does not easily yield the solutions, so we will use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

For our quadratic equation, a = 2, b = -5, and c = -6. Plugging in these values, we get:

x = (-(-5) ± sqrt((-5)^2 - 4(2)(-6))) / (2(2))
= (5 ± sqrt(25 + 48)) / 4
= (5 ± sqrt(73)) / 4

Now we can round to the nearest hundredth:

x ≈ 0.89 (rounded to the nearest hundredth)
x ≈ -1.03 (rounded to the nearest hundredth)

Therefore, the solutions to the quadratic equation 2x^2 - 5x = 6 are x ≈ 0.89 and x ≈ -1.03.