what two numbers multiply to give 324 but add to make -77?
a * b =324, a+b=-77, solve for a,b
a=-4.46693
b=-72.53317
I think your teacher or your book expected two simple whole integers, which are:
-81 x 4 = - 324
-81 + 4=-77
But it doesn't work for 324 because it gives a negative answer. Unless you made a mistake?.
+1904 \(x\times y=324\)
\(x+y=-77\)
There are several ways to solve this problem. I will solve this problem this way,
Solve for x in the first equation
\(x\times y=324\)
\(x\times \frac{y}{y}=\frac{324}{y}\)
\(x\times 1=\frac{324}{y}\)
\(x=\frac{324}{y}\)
Subsitute \(\frac{324}{y}\) for x in the second equations and solve for y.
\(\frac{334}{y}+y=-77\)
\(\frac{334}{y}\times y+y\times y=-77\times y\)
\(\frac{334\times y}{y}+y\times y=-77\times y\)
\(334+y\times y=-77\times y\)
\(334+y^2=-77\times y\)
\(334+y^2=-77y\)
\(334+y^2+77y=-77y+77y\)
\(334+y^2+77y=0\)
\(y^2+77y+334=0\)
\(y^2+77y+334-334=0-334\)
\(y^2+77y+0=0-334\)
\(y^2+77y+0=-334\)
\(y^2+77y+0+1482.25 =-334+ 1482.25\)
\(y^2+77y+1482.25 =-334+ 1482.25\)
\(y^2+77y+1482.25 = 1148.25\)
\((y+ 38.5 )^2= 1148.25\)
\((\sqrt{y+ 38.5})^2=\sqrt{1148.25}\)
\(y+ 38.5=±\sqrt{1148.25}\)
\(y+ 38.5≈±\ 33.8858377497148505\)
\(y+ 38.5≈ 33.8858377497148505\) and \(y+ 38.5≈- 33.8858377497148505\)
\(y+ 38.5-38.5≈ 33.8858377497148505-38.5\)and \(y+ 38.5-38.5≈ -33.8858377497148505-38.5\)
\(y+ 0≈ 33.8858377497148505-38.5\) and \(y+ 0≈ -33.8858377497148505-38.5\)
\(y≈ 33.8858377497148505-38.5\) and \(y≈ -33.8858377497148505-38.5\)
\(y≈-4.6141622502851495\) and \(y≈-72.3858377497148505\)
Subsitute y in the second equation and solve for x.
\(x+(-4.6141622502851495)≈-77\) and \(x+(-72.3858377497148505)≈-77\)
\(x-4.6141622502851495≈-77\) and \(x-72.3858377497148505≈-77\)
\(x-4.6141622502851495+4.6141622502851495≈-77+4.6141622502851495\) and \(x-72.3858377497148505+72.3858377497148505≈-77+72.3858377497148505\)
\(x-0≈-77+4.6141622502851495\) and \(x-0≈-77+72.3858377497148505\)
\(x≈-77+4.6141622502851495\) and \(x≈-77+72.3858377497148505\)
\(x≈-72.3858377497148505\) and \(x≈-4.6141622502851495\)
