Completing the square?

Question

3x^2+10x+13

Can you show me steps on how to do this please?

Answer 1

3(x^2+10/3 x) +13
=3(x^2 +10/3 x + 25/9) - 25/3 +13
=3(x+5/3)^2 +(39-25)/3
=3(x+5/3)^2 +14/3
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hint
to complete square
take the coefficient of x^2 as a common factor
then add square of 1/2 of coefficient of x +/-
coefficient of x is 10/3 1/2 of 10/3 =5/3 square of 5/3 is 25/9
so add +/-25/9

Answer 2

3 [ x ² + (10/3) x + 13/3 ]
3 [x² + (10/3)x + 25/9) - 25/9 + 39/9 ]
3 [ (x + 5/3)² + 14/9 ]

Answer 3

x = (-b +- (sqrt(b^2)) -4ac) /2a
Therefore:
x = (-10 +- sqrt(10^2 -4(3)(13))) / 2(3)
x = (-10 +- sqrt(100 -156)) / 6
x = (-10 +- sqrt(-56)) / 6
Since square root of -56 is not applicable, there are no real roots for this quadratic equation.