what number multiplys to get -30 but adds to get -11

Answer 1

WATCH THE SIGNS!!!!!

XY=-30

X+Y = -11 ---> Y = -11 - x

x(-11-x)= -30

-11x - x^2 = -30

x^2 + 11x - 30 = 0

[-11 +or- sqrt ( 121 + 4*30)]2 =

[-11 +or- sqrt(241)]/2=

[sqrt(241) - 11 ]/2

-([sqrt(241) +11)/2

I get the feeling you are off by a negative sign somewhere and are really looking for

-6 * -5 = +30 and -6 + -5 = -11

Answer 2

Mark M. is correct in his comment that 2 numbers needed for multiplication.

I'll assume you know that and are looking for 2 number A and B such that A*B = -30 and A+B=-11.

If A+B = -11, then A = -11 -B. Use this substitution for A in the multiplication.

A*B becomes (-11 - B) * B = -30

-11B -B² = -30

Add -11B -B² to both sides getting

B² + 11B - 30 = 0 (1)

Use the quadratic formula with a=1, b=11 and c= -30, to find 2 possible values of B solving the equation.

(-b =/- sqrt(b² - 4ac))/2a

Plug in values of a, b and c to get

(-11 +/- sqrt(121 - (-120)))/2 ==> (-11 +/- sqrt(241))/2 = 2.262 and -13.262

Note that -13.262 + 2.262 = -11 and -13.262 * 2.262 = -29.9998 ~ -30 (the product is not -30 due to rounding error)