Square root 2

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

Result

m1 =  3
m2 =  -3

Solution:

x=7 3m2+22−x=0 3m2+22−7=0 3m2+22=7  3m2+22=72  3m2−27=0  a=3;b=0;c=−27 D=b2−4ac=02−4⋅3⋅(−27)=324 D>0  m1,2=−b±D2a=±3246 m1,2=±186 m1,2=±3 m1=3 m2=−3   Factored form of the equation:  m1=3(m−3)(m+3)=0m1=3x = 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 -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: } \ \\ m_{1}=3 (m -3) (m +3) = 0m_{ 1 } = 3

Checkout calculation with our calculator of quadratic equations.

m2=(−3)=−3m_{ 2 } = (-3) = -3

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