Question

4x squared + 29x + 30=0

Answer 1

So for this equation we're going to complete the square.

Firstly, what two terms have a product of 120x^2 and a sum of 29x? 24x and 5x. Replace 29x with 24x + 5x: $4x^2+24x+5x+30=0$

Next, factor 4x^2 + 24x and 5x + 30 separately. Make sure that they have the same quantity inside the parentheses: $4x(x+6)+5(x+6)=0$

Now you can rewrite the equation as: $(4x+5)(x+6)=0$

Now using zero product property, solve for x:

$4x+5=0\\ 4x=-5\\ x=-1.25\\ \\ x+6=0\\ x=-6$

In short, x = -1.25 and -6