Step-by-step explanation:
Part 1)
The equation by factorization is
x^{2}+12x-230=(x-(-6+\sqrt{266}))(x-(-6-\sqrt{266}))x
2
+12x−230=(x−(−6+
266
))(x−(−6−
266
))
Both values of x are
x1=-6+\sqrt{266}x1=−6+
266
x2=-6-\sqrt{266}x2=−6−
266
Part 2) The dimensions of the cuboid are
4\ cm4 cm , (-5+\sqrt{266})\ cm(−5+
266
) cm and (5+\sqrt{266})\ cm(5+
266
) cm
Step-by-step explanation:
step 1
we know that
The volume of the cuboid is equal to
V=LWHV=LWH
substitute the given values
V=4(x+1)(x+11)V=4(x+1)(x+11)
V=924\ cm^{3}V=924 cm
3
so
\begin{gathered}4(x+1)(x+11)=924\\4(x^{2}+11x+x+11)=924\\ 4(x^{2}+12x+11)=924\\x^{2}+12x+11=231\\x^{2}+12x-230=0\end{gathered}
4(x+1)(x+11)=924
4(x
2
+11x+x+11)=924
4(x
2
+12x+11)=924
x
2
+12x+11=231
x
2
+12x−230=0
Complete the square
x^{2}+12x-230=0x
2
+12x−230=0
x^{2}+12x=230x
2
+12x=230
x^{2}+12x+36=230+36x
2
+12x+36=230+36
(x+6)^{2}=266(x+6)
2
=266
square root both sides
x+6=(+/-)\sqrt{266}x+6=(+/−)
266
x=-6(+/-)\sqrt{266}x=−6(+/−)
266
so
x1=-6+\sqrt{266}x1=−6+
266
x2=-6-\sqrt{266}x2=−6−
266
therefore
The equation by factorization is
x^{2}+12x-230=(x-(-6+\sqrt{266}))(x-(-6-\sqrt{266}))x
2
+12x−230=(x−(−6+
266
))(x−(−6−
266
))
step 2
Find the dimensions of the cuboid
The dimensions are
4\ cm4 cm
(x+1)\ cm ----- > (-6+\sqrt{266}+1)=(-5+\sqrt{266})\ cm(x+1) cm−−−−−>(−6+
266
+1)=(−5+
266
) cm
(x+11)\ cm ---- > (-6+\sqrt{266}+11)=(5+\sqrt{266})\ cm(x+11) cm−−−−>(−6+
266
+11)=(5+
266
) cm
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