|√x + 4x+ 3 | +(2x+ 5)=0 find the x value
Answers
Step-by-step explanation:
STEP
1
:
Isolate a square root on the left hand side
Original equation
√4-x+√x+9 = 5
Isolate
√4-x = -√x+9+5
STEP
2
:
Eliminate the radical on the left hand side
Raise both sides to the second power
(√4-x)2 = (-√x+9+5)2
After squaring
4-x = x+9+25-10√x+9
STEP
3
:
Get remaining radical by itself
Current equation
4-x = x+9+25-10√x+9
Isolate radical on the left hand side
10√x+9 = -4+x+x+9+25
Tidy up
10√x+9 = 30+2x
STEP
4
:
Eliminate the radical on the left hand side
Raise both sides to the second power
(10√x+9)2 = (30+2x)2
After squaring
100x+900 = 4x2+120x+900
STEP
5
:
Solve the quadratic equation
Rearranged equation
4x2 + 20x = 0
This equation has two rational roots:
{x1, x2}={0, -5}
STEP
6
:
Check that the first solution is correct
Original equation, root isolated, after tidy up
√4-x = -√x+9+5
Plug in 0 for x
√4-(0) = -√(0)+9+5
Simplify
√4 = 2
Solution checks !!
Solution is:
x = 0
STEP
7
:
Check that the second solution is correct
Original equation, root isolated, after tidy up
√4-x = -√x+9+5
Plug in -5 for x
√4-(-5) = -√(-5)+9+5
Simplify
√9 = 3
Solution checks !!
Solution is:
x = -5
Two solutions were found :
x = -5
x = 0