Using the quadratic formula, solve for x. A triangle has three angles that measure: (x+17), (3x+28), ?.The exterior angle next to ? is (x^2). What's x

The first step is to set up 2
equations.

The first is the sum of the interior
angles.

(x+17)+(3x+28)+y=180

The
second is the addition of 2 adjacent angles.

x^2 + y =
180

Solve the 2nd equation for
y.

y=180-x^2

Then substitue
into equation 1
giving

(x+17)+(3x+28)+(180-x^2)=180

by
combining like terms you
get

-x^2+4x+225=180

Subtract
180 from both
sides

-x^2+4x+45=0

Multiple
both sides by -1 in order to get x^2 term
positive

x^2-4x-45=0

Now use
quadratic formula

x=(-(-4) (+/-)
sqrt(-4^2-4*1*-45))/(2*1)

simplified

[4
(+/-)
sqrt(196)]/2

[4+/-14]/2

-10/2
= -5     18/2 = 9   answer cannot be negative so x = 9