Your answer is correct. Both base angles for that triangle are equal, meaning it is an isosceles triangle, and both the sides will have the same measure.
Answer:
x=7−√10 or x=7+√10
Step-by-step explanation:
−5(x−7)2+30=−20
Step 1: Simplify both sides of the equation.
−5x2+70x−215=−20
Step 2: Subtract -20 from both sides.
−5x2+70x−215−(−20)=−20−(−20)
−5x2+70x−195=0
For this equation: a=-5, b=70, c=-195
−5x2+70x+−195=0
Step 3: Use quadratic formula with a=-5, b=70, c=-195.
x=
−b±√b2−4ac
2a
x=
−(70)±√(70)2−4(−5)(−195)
2(−5)
x=
−70±√1000
−10
x=7−√10 or x=7+√10
The best way is to recognise that, if
x
=
5
is a root, then
x
−
5
=
0
, and ditto for the other two roots. So we have
x
−
5
,
x
−
i
,
x
+
i
all equalling zero. To find our polynomial, we just multiply the three terms together:
(
x
−
5
)
(
x
−
i
)
(
x
+
i
)
=
(
x
2
−
i
x
−
5
x
+
5
i
)
(
x
+
i
)
=
x
3
+
i
x
2
−
i
x
2
−
(
i
2
)
x
−
5
x
2
−
5
i
x
+
5
i
x
+
5
i
2
which simplifies to
x
3
−
5
x
2
+
x
−
5
.
