Question 194819
Solve equation for x.(Please step-by-step so i can undersatnd it thanks.)
sqrt(3x+54)+6=2
:
Step 1: Isolate the radical on the left side of the equation. Show your work.
{{{sqrt(3x+54)}}} + 6 = 2
Subtract 6 from both sides
{{{sqrt(3x+54)}}} = 2 - 6
{{{sqrt(3x+54)}}} = -4; that isolates the radical on the left
:
Step 2: Square both sides of the equation from step 1. Show your work.
{{{(sqrt(3x+54))^2}}} = {{{(-4)^2}}}
3x + 54 = 16; squaring a radical gets rid of it
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Step 3: Solve the equation from step 2 for x. Show your work.
3x + 54 = 16
Subtract 54 from both sides
3x = 16 - 54
3x = -38
Divide both sides by 3
x = {{{(-38)/3}}}
x = -12{{{2/3}}}
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Step 4: Check your solution from step 3 in the original equation. Show your work.
Use {{{-38/3}}} for substitution in the original equation
{{{sqrt(3(-38/3)+54)}}} + 6 = 2
note that the 3's cancel and we have
{{{sqrt(-38+54)}}} + 6 = 2
:
{{{sqrt(16)}}} + 6 = 2
 4 + 6 does not = 2, therefore there is no solution:
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Step 5: State the solution for the equation sqrt(3x+54)+6=2. There is none