Question

Solve the following equation by completing the square.

6m2 + 5m -3 = 0

* i need to put it in the box thingy *

Answer 1

`6m^2 + 5m - 3 = 0`

`6m^2 + 5m = 3`

Divide both sides by 6:

`m^2 + (5/6) m = 1/2`

Add (5/12)^2 to both sides.

`m^2 + (5/6) m + (5/12)^2 = 1/2 + (5/12)^2`

We engineered the left side to be a square. Simplify the right:

`(m + 5/12)^2 = 97/144`

Take square roots, remembering the plus/minus:

`m + 5/12 = \pm √(97/144)`

97 has no square factors,

`m + 5/12 = \pm √(97)/12`

`m = (-5 \pm √(97))/(12)`

That's the answer; how you fit it into the boxes I'll leave to you.

Check:

Let's check with the quadratic formula:

`m = (-5 \pm √(5^2 - 4(6)(-3)))/(12) = (-5 \pm √(97))/(12) \quad\checkmark`