# Square root 2

If the square root of 3m2 +22 and -x = 0, and x=7, what is m?

Correct result:

m1 =  3
m2 =  -3

#### Solution:

$x=7 \ \\ \sqrt{ 3m^2 +22 } - x=0 \ \\ \sqrt{ 3m^2 +22 } - 7=0 \ \\ \sqrt{ 3m^2 +22 }=7 \ \\ \ \\ 3m^2 +22=7^2 \ \\ 3m^2 +22=49 \ \\ \ \\ 3m^2 -27=0 \ \\ \ \\ a=3; b=0; c=-27 \ \\ D=b^2 - 4ac=0^2 - 4\cdot 3 \cdot (-27)=324 \ \\ D>0 \ \\ \ \\ m_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ \pm \sqrt{ 324 } }{ 6 } \ \\ m_{1,2}=\dfrac{ \pm 18 }{ 6 } \ \\ m_{1,2}=\pm 3 \ \\ m_{1}=3 \ \\ m_{2}=-3 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 3 (m -3) (m +3)=0 \ \\ m_{1}=3$

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