Answer:
x = -3
Step-by-step explanation:
Radical Equation entered :
√2x+6+√x+4 = 1
Step by step solution :
STEP
1
:
Isolate a square root on the left hand side
Original equation
√2x+6+√x+4 = 1
Isolate
√2x+6 = -√x+4+1
STEP
2
:
Eliminate the radical on the left hand side
Raise both sides to the second power
(√2x+6)2 = (-√x+4+1)2
After squaring
2x+6 = x+4+1-2√x+4
STEP
3
:
Get remaining radical by itself
Current equation
2x+6 = x+4+1-2√x+4
Isolate radical on the left hand side
2√x+4 = -2x-6+x+4+1
Tidy up
2√x+4 = -x-1
STEP
4
:
Eliminate the radical on the left hand side
Raise both sides to the second power
(2√x+4)2 = (-x-1)2
After squaring
4x+16 = x2+2x+1
STEP
5
:
Solve the quadratic equation
Rearranged equation
x2 - 2x -15 = 0
This equation has two rational roots:
{x1, x2}={5, -3}
STEP
6
:
Check that the first solution is correct
Original equation, root isolated, after tidy up
√2x+6 = -√x+4+1
Plug in 5 for x
√2•(5)+6 = -√(5)+4+1
Simplify
√16 = -2
Solution does not check
4 ≠ -2
STEP
7
:
Check that the second solution is correct
Original equation, root isolated, after tidy up
√2x+6 = -√x+4+1
Plug in -3 for x
√2•(-3)+6 = -√(-3)+4+1
Simplify
√0 = 0
Solution checks !!
Solution is:
x = -3
