One more! Solve this equation + express radicals in simplest form?

6m^2 + 12m + 3 = 0
6(m^2 + 2m + 1) = 0
So, (m^2 + 2m + 1) = 0
(m + 1)^2 = 0
m+1 = 0
m= -1

6m² + 12m + 3 = 0
m² + m = - 1/2 + 1²
m² + m = - 1/2 + 2/2
(m + 1)² = 1/2
m + 1 = +/- 0.7071068

m = 0.7071068 - 1, m = - 0.2928932
m = - 0.7071068 - 1, m = - 1.7071068

Answer: m = - 0.2928932, - 1.7071068

Proof (m = - 0.2928932):
6(- 0.2928932)² + 12(- 0.2928932) = - 3
6(0.0857864) - 3.5147184 = - 3
0.5147184 - 3.5147184 = - 3
- 3 = - 3

Proof (m = - 1.7071068):
6(- 1.7071068)² + 12(- 1.7071068) = - 3
6(2.9142136) - 20.485281 = - 3
17.485281 - 20.485281 = - 3
- 3 = - 3

hi Loop, rearrange as 3n^2 +8n + 3 = 0 Use the technique of having root as [-b+or-./(b^2-4ac)] / 2a here a = 3, b = 8 and c = 3 So [-8 +or- ./ (sixty 4-36)] / 6 It includes be (-4 + ./7) / 3 and (-4 - ./7) / 3 2) increasing, 4m^2 - 4m + a million = -9 Or 4m^2 - 4m + 10 Simplified as 2m^2 - 2m + 5 = 0 same way we get, (2 + 3i) / 2 and (2-3i) / 2 So the roots are complicated roots. of direction for the final one ie 6) x^2 - x - 20 = 0 could desire to be factorized as (x-5) (x+4) = 0 So answer is x = 5 or -4 In case of 5, purely multiply via out by using 24, you get 8y^2 - 2y -a million = 0 this could properly be factorized as (2y-a million)(4y+a million) so y = a million/2 or -a million/4 desire you're able to do the others on your guy or woman.

6m^2 + 12m + 3 = 0
2m^2 + 4m + 1 = 0
m = [-b ±√(b^2 - 4ac)]/(2a)

a = 2
b = 4
c = 1

m = [-4 ±√(16 - 8)]/4
m = [-4 ±√8]/4
m = [-4 ±√(2^2 * 2)]/4
m = [-4 ±2√2]/4
m = -4/4 ±(2√2)/4
m = -1 ±(√2)/2

∴ m = -1 ±(√2)/2

Use quadratic formula and simplify.
imho...

m=[-6+&-(36-18)^1/2]/6=
=-1-(\/''2)/2 & -1+(\/'''2'')/2