<span>sqrt(3x+7)=x-1 </span>One solution was found : <span> x = 6
</span>Radical Equation entered :
<span> √3x+7 = x-1
</span>
Step by step solution :<span>Step 1 :</span>Isolate the square root on the left hand side :
Radical already isolated
<span> √3x+7 = x-1
</span>
<span>Step 2 :</span>Eliminate the radical on the left hand side :
Raise both sides to the second power
<span> (√3x+7)2 = (x-1)2
</span> After squaring
<span> 3x+7 = x2-2x+1
</span>
<span>Step 3 :</span>Solve the quadratic equation :
Rearranged equation
<span> x2 - 5x -6 = 0
</span>
This equation has two rational roots:
<span> {x1, x2}={6, -1}
</span>
<span>Step 4 :</span>Check that the first solution is correct :
Original equation
<span> √3x+7 = x-1
</span> Plug in 6 for x
<span> √3•(6)+7 = (6)-1
</span> Simplify
<span> √25 = 5
</span> Solution checks !!
Solution is:
<span> x = 6
</span>
<span>Step 5 :</span>Check that the second solution is correct :
Original equation
<span> √3x+7 = x-1
</span> Plug in -1 for x
<span> √3•(-1)+7 = (-1)-1
</span> Simplify
<span> √4 = -2
</span> Solution does not check
2 ≠ -2
One solution was found : <span> x = 6</span>
