16x *52xsquare*125xcube
going to mark brainliest for the correct answer
Answers
Answer:
Step 1: Isolate the radical term.
Before we take the square of both sides, we need to isolate the radical term.
\begin{aligned}6+3x&=\sqrt{2x+12}+2x\\\\ 6+x&=\sqrt{2x+12}\\\\ \end{aligned}
6+3x
6+x
=
2x+12
+2x
=
2x+12
Step 2: Take the square of both sides.
Now that we have isolated the radical term, we can square both sides to eliminate the radical:
\begin{aligned}6+x&=\sqrt{2x+12}\\\\ \left(6+x\right)^{\blueD{2}}&=\left(\sqrt{2x+12}\right)^{\blueD{2}}\\\\ 36+12x+x^2&=2x+12\\\\ x^2+10x+24&=0\\\\ (x+6)(x+4)&=0 \end{aligned}
6+x
(6+x)
2
36+12x+x
2
x
2
+10x+24
(x+6)(x+4)
=
2x+12
=(
2x+12
)
2
=2x+12
=0
=0
We found two possible solutions: x=-6x=−6x, equals, minus, 6 and x=-4x=−4x, equals, minus, 4.
Step 3: Check for extraneous solutions.
The original equation is 6+3x=\sqrt{2x+12}+2x6+3x=
2x+12
+2x6, plus, 3, x, equals, square root of, 2, x, plus, 12, end square root, plus, 2, x.
When \maroonD{x}=\maroonD{-6}x=−6start color #ca337c, x, end color #ca337c, equals, start color #ca337c, minus, 6, end color #ca337c, we get:
\begin{aligned}6+3\maroonD{x}&=\sqrt{2\maroonD{x}+12}+2\maroonD{x}\\\\ 6+3(\maroonD{-6})&\stackrel{?}=\sqrt{2(\maroonD{-6})+12}+2(\maroonD{-6})\\\\ -12&\stackrel{?}=\sqrt{0}-12\\\\ -12&\stackrel{?}=0-12\\\\ -12&=-12 \end{aligned}
6+3x
6+3(−6)
−12
−12
−12
=
2x+12
+2x
=
?
2(−6)+12
+2(−6)
=
?
0
−12
=
?
0−12
=−12
So x=-6x=−6x, equals, minus, 6 is indeed a solution.
When \maroonD{x}=\maroonD{-4}x=−4start color #ca337c, x, end color #ca337c, equals, start color #ca337c, minus, 4, end color #ca337c, we get:
\begin{aligned}6+3\maroonD{x}&=\sqrt{2\maroonD{x}+12}+2\maroonD{x}\\\\ 6+3(\maroonD{-4})&\stackrel{?}=\sqrt{2(\maroonD{-4})+12}+2(\maroonD{-4})\\\\ -6&\stackrel{?}=\sqrt{4}-8\\\\ -6&\stackrel{?}=2-8\\\\ -6&=-6 \end{aligned}
6+3x
6+3(−4)
−6
−6
−6
=
2x+12
+2x
=
?
2(−4)+12
+2(−4)
=
?
4
−8
=
?
2−8
=−6
So x=-4x=−4x, equals, minus, 4 is a solution too!
Conclusion
We found that this equation has two solutions! Both x=-6x=−6x, equals, minus, 6 and x=-4x=−4x, equals, minus, 4 solve the equation.
Explanation:
Hope it helps you :)