x=2
Step-by-step explanation:
Step by step solution :
Step 1 :
Isolate a square root on the left hand side :
Original equation
√9x+7+√2x = 7
Isolate
√9x+7 = -√2x+7
Step 2 :
Eliminate the radical on the left hand side :
Raise both sides to the second power
(√9x+7)2 = (-√2x+7)2
After squaring
9x+7 = 2x+49-14√2x
Step 3 :
Get remaining radical by itself :
Current equation
9x+7 = 2x+49-14√2x
Isolate radical on the left hand side
14√2x = -9x-7+2x+49
Tidy up
14√2x = -7x+42
Step 4 :
Eliminate the radical on the left hand side :
Raise both sides to the second power
(14√2x)2 = (-7x+42)2
After squaring
392x = 49x2-588x+1764
Step 5 :
Solve the quadratic equation :
Rearranged equation
49x2 - 980x + 1764 = 0
This equation has two rational roots:
{x1, x2}={18, 2}
Step 6 :
Check that the first solution is correct :
Original equation, root isolated, after tidy up
√9x+7 = -√2x+7
Plug in 18 for x
√9•(18)+7 = -√2•(18)+7
Simplify
√169 = 1
Solution does not check
13 ≠ 1
Step 7 :
Check that the second solution is correct :
Original equation, root isolated, after tidy up
√9x+7 = -√2x+7
Plug in 2 for x
√9•(2)+7 = -√2•(2)+7
Simplify
√25 = 5
Solution checks !!
Solution is:
x = Step by step solution :
Step 1 :
Isolate a square root on the left hand side :
Original equation
√9x+7+√2x = 7
Isolate
√9x+7 = -√2x+7
Step 2 :
Eliminate the radical on the left hand side :
Raise both sides to the second power
(√9x+7)2 = (-√2x+7)2
After squaring
9x+7 = 2x+49-14√2x
Step 3 :
Get remaining radical by itself :
Current equation
9x+7 = 2x+49-14√2x
Isolate radical on the left hand side
14√2x = -9x-7+2x+49
Tidy up
14√2x = -7x+42
Step 4 :
Eliminate the radical on the left hand side :
Raise both sides to the second power
(14√2x)2 = (-7x+42)2
After squaring
392x = 49x2-588x+1764
Step 5 :
Solve the quadratic equation :
Rearranged equation
49x2 - 980x + 1764 = 0
This equation has two rational roots:
{x1, x2}={18, 2}
Step 6 :
Check that the first solution is correct :
Original equation, root isolated, after tidy up
√9x+7 = -√2x+7
Plug in 18 for x
√9•(18)+7 = -√2•(18)+7
Simplify
√169 = 1
Solution does not check
13 ≠ 1
Step 7 :
Check that the second solution is correct :
Original equation, root isolated, after tidy up
√9x+7 = -√2x+7
Plug in 2 for x
√9•(2)+7 = -√2•(2)+7
Simplify
√25 = 5
Solution checks !!
Solution is:
x = 2
