solve for x.√(4x+9)+x=9
Answers
Answer:
Mark my answer brainliest
Step-by-step explanation:
Radical Equation entered :
x-9 = √4x+9
Step by step solution :
STEP
1
:
Isolate the square root on the left hand side
Original equation
x-9 = √4x+9
Isolate
-√4x+9 = -x+9
Tidy up
√4x+9 = x-9
STEP
2
:
Eliminate the radical on the left hand side
Raise both sides to the second power
(√4x+9)2 = (x-9)2
After squaring
4x+9 = x2-18x+81
STEP
3
:
Solve the quadratic equation
Rearranged equation
x2 - 22x + 72 = 0
This equation has two rational roots:
{x1, x2}={18, 4}
STEP
4
:
Check that the first solution is correct
Original equation, root isolated, after tidy up
√4x+9 = x-9
Plug in 18 for x
√4•(18)+9 = (18)-9
Simplify
√81 = 9
Solution checks !!
Solution is:
x = 18
STEP
5
:
Check that the second solution is correct
Original equation, root isolated, after tidy up
√4x+9 = x-9
Plug in 4 for x
√4•(4)+9 = (4)-9
Simplify
√25 = -5
Solution does not check
5 ≠ -5
One solution was found :
x = 18