Math 12 - Review - Quadratic

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Could someone please show me ALL the steps to do the following:

Equation: 2x^2 = 11

Answer: Square root of 22 over 2, Negative square root of 22 over 2; 2.35, -2.35

Equation: 3m^2 - 4m = -2

Answer: 2 +/- i (imaginary sign) square root of 2 over 3

• Math 12 - Review - Quadratic -

The first:
x2</sup?=11/2
x= sqrt (11/2) which is an ok answer. Some purists don't like sqare roots of fractions, so ...
x= sqrt [(11/2)(2/2)]
x= sqrt (22/4)= 1/2 sqrt 22

On the last, change it to a quadratic..
3m2 -4m + 2=0

x= (4 +- sqrt (16-24))/6

x= 2/3 +- [sqrt (-8)]/6

x= 2/3 +- sqrt (-8/36)
then reduce that (the second part reduces to sqrt (-2/9) or 1/3 sqrt -2

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