Question

If m^2-5/2m=-11/2,m=

Plz answer fast!!!

Answer 1

`m = \frac { 5 } { 4 } \pm\frac { 3 } { 4 } i \sqrt { 7 }`

Explanation:

We are given the following equation and we are to solve it for m:

`m ^ 2 - \frac { 5 } { 2 } m = - \frac { 1 1 } { 2 }`

We will solve this using the quadratic formula
`(-b\±√(b^2-4ac))/(2a)`.

Rearranging the equation to get:

`m^2-(5)/(2)m+(11)/(2)=0`

Substituting the given values in the above formula to get:

`m=\frac{-(-(5)/(2))\±\sqrt{(-(5)/(2))^2-4(1)((11)/(2))}}{2*1}\\\\m=\frac{(5)/(2)\±\sqrt{-(63)/(4)}}{2}`

We know that
`√(-1)=i`.

`m=((5)/(2)\±(3)/(2)i√(7))/(2)\\\\m=(5)/(4)\±(3)/(4)i√(7)`

Answer 2

Answer:
`m=(5)/(4)\±(3)/(4)i√(7)`

Explanation:

Use the Quadratic formula:

`m=(-b\±√(b^2)-4ac)/(2a)`

Given the quadratic equation
`m^2-(5)/(2)m=-(11)/(2)`

Make it equal to zero:

`m^2-(5)/(2)m+(11)/(2)=0`

You can see that :

`a=1\\b=-(5)/(2)\\\\c=(11)/(2)`

Substitute values:

`m=\frac{-(-(5)/(2))\±\sqrt{(-(5)/(2))^2-4(1)((11)/(2))}}{2*1}\\\\m=\frac{(5)/(2)\±\sqrt{-(63)/(4)}}{2}\\\\m=((5)/(2)\±(3)/(2)i√(7))/(2)\\\\m=(5)/(4)\±(3)/(4)i√(7)`

(Remember that
`√(-1)=i`)