Solve the equation. \sqrt{3x+1}-\sqrt{x+4}=1

Ronnie Baur

Ronnie Baur

Answered question

2021-11-16

Solve the equation. 3x+1x+4=1

Answer & Explanation

SaurbHurbkj

SaurbHurbkj

Beginner2021-11-17Added 16 answers

Step 1
Given equation is 3x+1x+4=1.
Step 2
Solve for x.
3x+1x+4=1
3x+1=1+x+4
(3x+1)2=(1+x+4)2
3x+1=1+x+4+2x+4
2x4=2x+4
(2x4)2=(2x+4)2
4x216x+16=4(x+4)
4x216x+16=4x+16
4x220x=0
4x(x-5)=0
x=0,5
Step 3
Check the result.
3x+1x+4=1
00+4=1
0-2=1
-2=1 False
3x+1x+4=1
15+15+4=
169=1
4-3=1
1=1 True
Thus, x=5.
Witheyesse47

Witheyesse47

Beginner2021-11-18Added 14 answers

Step 1: Isolate a square root on the left hand side
Original equation
3x+1x+4=1
Isolate
3x+1=x+4+1
Step 2: Eliminate the radical on the left hand side
Raise both sides to the second power
(3x+1)2=(x+4+1)2
After squaring
3x+1=x+4+1+2x+4
Step 3: Get remaining radical by itself
Current equation
3x+1=x+4+1+2x+4
Isolate radical on the left hand side
2x+4=3x1+x+4+1
Tidy up
2x+4=2x4
Step 4: Eliminate the radical on the left hand side
Raise both sides to the second power
(2x+4)2=(2x4)2
After squaring
4x+16=4x216x+16
Step 5: Solve the quadratic equation
Rearranged equation
4x220x=0
This equation has two rational roots:
{x1,x2}={5,0}
Step 6: Check that the first solution is correct
Original equation, root isolated, after tidy up
3x+1=x+4+1
Plug in 5 for x
3(5)+1=(5)+4+1
Simplify
16=4
Solution is:
x=5
Step 7: Check that the second solution is correct
Original equation, root isolated, after tidy up
3x+1=x+4+1
Plug in 0 for x
3(0)+1=(0)+4+1
Simplify
1=3
Solution does not check
13
One solution was found:
x=5

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