Question

5x2+90x+405=0

Answer 1

I'd start by dividing out any common factors in the coefficients

Answer 2

the two is supposed to be a squared

Answer 3

x = -9

Answer 4

Is what i got

Answer 5

But I did it mentally so do the equation to check it.

Answer 6

nope

Answer 7

\[5x^2+5*18x+5*81 = 0\]\[x^2+18x+81=0\]This is a perfect square:
\[x^2+18x+81 = (x+9)^2\]\[(x+9)^2=0\]\[x+9 = 0\]\[x = -9\]

Test our solution:
\[5(-9)^2 + 90(-9) + 405 = 0\]\[5*81-810+405 = 0\]\[405-810+405 = 0\]\[405+405-810 = 0\]\[810-810=0\]\[0=0\checkmark\]

Answer 8

because this is a perfect square, both solutions are identical, and the quadratic formula reduces to \[x = -\frac{b}{2a}\]which you may recognize as the formula for the x-coordinate of the vertex of a parabola written in \(y = ax^2+bx+c\) form