Answer:
1 Expand.
{x}^{3}+{x}^{2}+5{x}^{2}+5x=42
x
3
+x
2
+5x
2
+5x=42
2 Simplify {x}^{3}+{x}^{2}+5{x}^{2}+5xx
3
+x
2
+5x
2
+5x to {x}^{3}+6{x}^{2}+5xx
3
+6x
2
+5x.
{x}^{3}+6{x}^{2}+5x=42
x
3
+6x
2
+5x=42
3 Move all terms to one side.
{x}^{3}+6{x}^{2}+5x-42=0
x
3
+6x
2
+5x−42=0
4 Factor {x}^{3}+6{x}^{2}+5x-42x
3
+6x
2
+5x−42 using Polynomial Division.
({x}^{2}+8x+21)(x-2)=0
(x
2
+8x+21)(x−2)=0
5 Solve for xx.
x=2
x=2
6 Use the Quadratic Formula.
1 In general, given a{x}^{2}+bx+c=0ax
2
+bx+c=0, there exists two solutions where:
x=\frac{-b+\sqrt{{b}^{2}-4ac}}{2a},\frac{-b-\sqrt{{b}^{2}-4ac}}{2a}
x=
2a
−b+
b
2
−4ac
,
2a
−b−
b
2
−4ac
2 In this case, a=1a=1, b=8b=8 and c=21c=21.
{x}^{}=\frac{-8+\sqrt{{8}^{2}-4\times 21}}{2},\frac{-8-\sqrt{{8}^{2}-4\times 21}}{2}
x
=
2
−8+
8
2
−4×21
,
2
−8−
8
2
−4×21
3 Simplify.
x=\frac{-8+2\sqrt{5}\imath }{2},\frac{-8-2\sqrt{5}\imath }{2}
x=
2
−8+2
5
,
2
−8−2
5
x=\frac{-8+2\sqrt{5}\imath }{2},\frac{-8-2\sqrt{5}\imath }{2}
x=
2
−8+2
5
,
2
−8−2
5
7 Collect all solutions from the previous steps.
x=2,\frac{-8+2\sqrt{5}\imath }{2},\frac{-8-2\sqrt{5}\imath }{2}
x=2,
2
−8+2
5
,
2
−8−2
5
8 Simplify solutions.
x=2,-4+\sqrt{5}\imath ,-4-\sqrt{5}\imath
x=2,−4+
5
,−4−
5
Step-by-step explanation:
the rectangle there is represent as I
then some number in there is doubled sorry
